Exhibit 5.1

[Skadden, Arps, Slate, Meagher & Flom LLP Letterhead]

June 12, 2020

Applied Therapeutics, Inc.
545 Fifth Avenue, Suite 1400
New York, New York 10017

Re: Applied Therapeutics, Inc.
Registration Statement on Form S-3

Ladies and Gentlemen:

We have acted as special United States counsel to Applied Therapeutics, Inc., a Delaware corporation (the “Company”), in connection with the registration statement on Form S-3 (File No. 333-238948) filed on June 4, 2020 with the Securities and Exchange Commission (the “Commission”) under the under the Securities Act of 1933 (the “Securities Act”) , and Pre-Effective Amendment No. 1 thereto to be filed by the Company with the Commission on the date hereof (such registration statement, as so amended, being hereafter referred to as the “Registration Statement”). The Registration Statement relates to the issuance and sale by the Company from time to time, pursuant to Rule 415 of the General Rules and Regulations of the Commission promulgated under the Securities Act (the “Rules and Regulations”), of (i) shares of common stock, par value $0.0001 per share, of the Company (“Common Stock”) , (ii) shares of preferred stock, par value $0.0001 per share, of the Company (“Preferred Stock”), which may be issued in one or more series, (iii) depositary receipts (the “Receipts”) representing fractional shares of Preferred Stock, which are called depositary shares (the “Depositary Shares”) and which may be issued pursuant to one or more depositary agreements (each, a “Depositary Agreement”) proposed to be entered into between the Company and one or more bank or trust companies to be named in the applicable Depositary Agreement (each, a “Bank Depositary”), (iv) debt securities of the Company (“Debt Securities”), which may be issued in one or more series under an indenture (the “Indenture”) proposed to be entered into by the Company and the trustee to be named therein, the form of which is filed as an exhibit to the Registration Statement, (v) warrants to purchase shares of Common Stock, shares of Preferred Stock or Debt Securities (“Warrants”), which may be issued pursuant to one or more warrant agreements (each, a “Warrant Agreement”) proposed to be entered into by the Company and one or more warrant agents to be named therein and (vi) such indeterminate number of shares of Common Stock, Preferred Stock or Depositary Shares and indeterminate amount of Debt Securities as may be issued upon conversion, exchange or exercise, as applicable, of any Preferred Stock, Depositary Shares, Debt Securities or Warrants, including such shares of Common Stock or Preferred Stock as may be issued pursuant to anti-dilution adjustments determined at the time of offering (collectively, “Indeterminate Securities”). The Common Stock, Preferred Stock, Depositary Shares, Debt Securities, Warrants and Indeterminate Securities offered pursuant to the Registration Statement are collectively referred to herein as the “Securities”.

We have also acted as special United States counsel to the Company in connection with the Equity Distribution Agreement, dated the date hereof (the “Equity Distribution Agreement”) by and between the Company and Goldman Sachs & Co. LLC (the “Manager”), relating to the offer and sale by the Company from time to time of shares (the “ATM Shares”) of Common Stock, having an aggregate gross sales price of up to $100,000,000 to or through the Manager as sales agent and/or principal.

Applied Therapeutics, Inc.

June 12, 2020

Page 2

This opinion is being furnished in accordance with the requirements of Item 601(b)(5) of Regulation S-K under the Securities Act.

In rendering the opinions stated herein, we have examined and relied upon the following:

(a)the Registration Statement;

(b)the prospectus (the “Base Prospectus”), which forms a part of and is included in the Registration Statement;

(c)the prospectus supplement (together with the Base Prospectus, the “Prospectus”), relating to the offering of the ATM Shares, which forms a part of and is included in the Registration Statement;

(d)the form of Indenture filed as an exhibit to the Registration Statement;

(e) an executed copy of the Equity Distribution Agreement;

(f)an executed copy of a certificate of Shoshana Shendelman, Secretary of the Company, dated the date hereof (the “Secretary’s Certificate”);

(g)a copy of the Company’s Amended and Restated Certificate of Incorporation as certified by the Secretary of State of the State of Delaware as of June 4, 2020, and certified pursuant to the Secretary’s Certificate (the “Certificate of Incorporation”);

(h)a copy of the Company’s Amended and Restated Bylaws in effect as of the date hereof and certified pursuant to the Secretary’s Certificate (the “Bylaws”); and

(i)a copy of certain resolutions of the Board of Directors of the Company, adopted on June 4, 2020, certified pursuant to the Secretary’s Certificate.

We have also examined originals or copies, certified or otherwise identified to our satisfaction, of such records of the Company and such agreements, certificates and receipts of public officials, certificates of officers or other representatives of the Company and others, and such other documents as we have deemed necessary or appropriate as a basis for the opinions stated below.

In our examination, we have assumed the genuineness of all signatures, the legal capacity and competency of all natural persons, the authenticity of all documents submitted to us as originals, the conformity to original documents of all documents submitted to us as facsimile, electronic, certified or photocopied copies, and the authenticity of the originals of such copies. As to any facts relevant to the opinions stated herein that we did not independently establish or verify, we have relied upon statements and representations of officers and other representatives of the Company and others and of public officials, including those in the Secretary’s Certificate.

We do not express any opinion with respect to the laws of any jurisdiction other than (i) the laws of the State of New York and (ii) the General Corporation Law of the State of Delaware (the “DGCL”) (all of the foregoing being referred to as “Opined on Law”).

Applied Therapeutics, Inc.

June 12, 2020

Page 3

As used herein, “Transaction Documents” means the Depositary Agreements, the Indenture and any supplemental indentures thereto, the Warrant Agreements and any applicable underwriting or purchase agreement.

The opinions stated in paragraphs 1 through 5 below presume that all of the following (collectively, the “general conditions”) shall have occurred prior to the issuance of the Securities referred to therein: (i) the Registration Statement, as finally amended (including all necessary post-effective amendments), has become effective under the Securities Act; (ii) an appropriate prospectus supplement or term sheet with respect to such Securities has been prepared, delivered and filed in compliance with the Securities Act and the applicable Rules and Regulations; (iii) the applicable Transaction Documents shall have been duly authorized, executed and delivered by the Company and the other parties thereto, including, if such Securities are to be sold or otherwise distributed pursuant to a firm commitment underwritten offering, the underwriting agreement or purchase agreement with respect thereto; (iv) the Board of Directors of the Company, including any duly authorized committee thereof, shall have taken all necessary corporate action to approve the issuance and sale of such Securities and related matters and appropriate officers of the Company have taken all related action as directed by or under the direction of the Board of Directors of the Company; and (v) the terms of the applicable Transaction Documents and the issuance and sale of such Securities have been duly established in conformity with the certificate of incorporation of the Company so as not to violate any applicable law, the certificate of incorporation of the Company or the bylaws of the Company, or result in a default under or breach of any agreement or instrument binding upon the Company, and so as to comply with any requirement or restriction imposed by any court or governmental body having jurisdiction over the Company.

Based upon the foregoing and subject to the qualifications and assumptions stated herein, we are of the opinion that:

1.       With respect to any shares of Common Stock (other than the ATM Shares, which are covered in paragraph 6 below) offered by the Company, including any Indeterminate Securities constituting Common Stock (the “Offered Common Stock”), when (a) the general conditions shall have been satisfied, (b) if the Offered Common Stock is to be certificated, certificates in the form required under the DGCL representing the shares of Offered Common Stock are duly executed and countersigned and (c) the shares of Offered Common Stock are registered in the Company’s share registry and delivered upon payment of the agreed-upon consideration therefor, the shares of Offered Common Stock, when issued and sold or otherwise distributed in accordance with the provisions of the applicable Transaction Document, will be duly authorized by all requisite corporate action on the part of the Company under the DGCL and validly issued, fully paid and nonassessable; provided that the consideration therefor is not less than $0.0001 per share of Common Stock.

2.       With respect to the shares of any series of Preferred Stock offered by the Company, including any Indeterminate Securities constituting Preferred Stock of such series (the “Offered Preferred Stock”), when (a) the general conditions shall have been satisfied, (b) the Board of Directors of the Company, or a duly authorized committee thereof, has duly adopted a Certificate of Designations for the Offered Preferred Stock in accordance with the DGCL (the “Certificate”), (c) the filing of the Certificate with the Secretary of State of the State of Delaware has duly occurred, (d) if the Offered Preferred Stock is to be certificated, certificates in the form required under the DGCL representing the shares of Offered Preferred Stock are duly executed and countersigned and (e) the shares of Offered Preferred Stock are registered in the Company’s share registry and delivered upon payment of the agreed-upon consideration therefor, the shares of Offered Preferred Stock, when issued and sold or otherwise distributed in accordance with the provisions of the applicable Transaction Document, will be duly authorized by all requisite corporate action on the part of the Company under the DGCL and validly issued, fully paid and nonassessable; provided that the consideration therefor is not less than $0.0001 per share of Preferred Stock.

Applied Therapeutics, Inc.

June 12, 2020

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3.       With respect to any Depositary Shares offered by the Company, including any Indeterminate Securities constituting Depositary Shares (the “Offered Depositary Shares”), when (a) the general conditions shall have been satisfied, (b) the Preferred Stock relating to such Offered Depositary Shares has been duly authorized for issuance by the Company; (c) the Offered Depositary Shares have been duly executed, delivered, countersigned, issued and sold in accordance with the provisions of the applicable Depositary Agreement, and the Offered Depositary Shares have been delivered to the Bank Depositary for deposit in accordance with the applicable Depositary Agreement; and (d) the Receipts evidencing the Depositary Shares have been duly issued against deposit of the related shares of Preferred Stock with the Bank Depositary in accordance with the applicable Depositary Agreement, such Depositary Agreement will constitute a legally valid and binding obligation of the Company, enforceable against the Company in accordance with its respective terms under the laws of the State of New York.

4.       With respect to any series of Debt Securities offered by the Company, including any Indeterminate Securities constituting Debt Securities of such series (the “Offered Debt Securities”), when (a) the general conditions shall have been satisfied, (b) the Indenture has been qualified under the Trust Indenture Act of 1939 (the “TIA”); (c) the issuance, sale and terms of the Offered Debt Securities and related matters have been approved and established in conformity with the applicable Transaction Documents and (d) the certificates evidencing the Offered Debt Securities have been issued in a form that complies with the provisions of the applicable Transaction Documents and have been duly executed and authenticated in accordance with the provisions of the Indenture and any other applicable Transaction Documents and issued and sold or otherwise distributed in accordance with the provisions of the applicable Transaction Document upon payment of the agreed-upon consideration therefor, the Offered Debt Securities will constitute valid and binding obligations of the Company, enforceable against the Company in accordance with their respective terms under the laws of the State of New York.

5.       With respect to any Warrants offered by the Company (the “Offered Warrants”), when (a) the general conditions shall have been satisfied, (b) the Common Stock, Preferred Stock and/or Debt Securities for which the Offered Warrants are exercisable have been duly authorized for issuance by the Company and (c) certificates evidencing the Offered Warrants have been duly executed, delivered and countersigned in accordance with the provisions of the applicable Warrant Agreement, the Offered Warrants, when issued and sold or otherwise distributed in accordance with the provisions of the applicable Transaction Document upon payment of the agreed-upon consideration therefor, will constitute valid and binding obligations of the Company, enforceable against the Company in accordance with their respective terms under the laws of the State of New York.

6.       When (a) the Registration Statement, as finally amended (including all necessary post-effective amendments), has become effective under the Securities Act, (b) if the ATM Shares are to be certificated, certificates in the form required under the DGCL representing the ATM Shares are duly executed and countersigned and (c) the ATM Shares are registered in the Company’s share registry, the ATM Shares will be duly authorized by all requisite corporate action on the part of the Company under the DGCL and when issued and sold in accordance with the Equity Distribution Agreement, will be validly issued, fully paid and nonassessable, provided that the consideration therefor is not less than $0.001 per share of Common Stock.

The opinions stated herein are subject to the following qualifications:

(a)        we do not express any opinion with respect to the effect on the opinions stated herein of any bankruptcy, insolvency, reorganization, moratorium, fraudulent transfer, preference and other similar laws or governmental orders affecting creditors’ rights generally, and the opinions stated herein are limited by such laws and by general principles of equity (regardless of whether enforcement is sought in equity or at law);

(b)        we do not express any opinion with respect to any law, rule or regulation that is applicable to any party to any Transaction Document or the transactions contemplated thereby solely because such law, rule or regulation is part of a regulatory regime applicable to any such party or any of its affiliates as a result of the specific assets or business operations of such party or such affiliates;

Applied Therapeutics, Inc.

June 12, 2020

Page 5

(c)       except to the extent expressly stated in the opinions contained herein, we have assumed that each of the Transaction Documents constitutes the valid and binding obligation of each party to such Transaction Document, enforceable against such party in accordance with its terms;

(d)       we do not express any opinion with respect to the enforceability of any provision contained in any Transaction Document relating to any indemnification, contribution, non-reliance, exculpation, release, limitation or exclusion of remedies, waiver or other provisions having similar effect that may be contrary to public policy or violative of federal or state securities laws, rules or regulations, or to the extent any such provision purports to, or has the effect of, waiving or altering any statute of limitations;

(e)       we do not express any opinion with respect to the enforceability of any provision of any Transaction Document to the extent that such section purports to bind the Company to the exclusive jurisdiction of any particular federal court or courts;

(f)        we call to your attention that irrespective of the agreement of the parties to any Transaction Document, a court may decline to hear a case on grounds of forum non conveniens or other doctrine limiting the availability of such court as a forum for resolution of disputes; in addition, we call to your attention that we do not express any opinion with respect to the subject matter jurisdiction of the federal courts of the United States of America in any action arising out of or relating to any Transaction Document;

(g)       we have assumed that any agent of service will have accepted appointment as agent to receive service of process and call to your attention that we do not express any opinion if and to the extent such agent shall resign such appointment. Further, we do not express any opinion with respect to the irrevocability of the designation of such agent to receive service of process;

(h)       we have assumed that the choice of New York law to govern the Indenture and any supplemental indenture thereto is a valid and legal provision;

(i)        we have assumed that the laws of the State of New York will be chosen to govern any Depositary Agreements or Warrant Agreements and that such choice is and will be a valid and legal provision;

(j)        we have assumed that the Indenture will be duly authorized, executed and delivered by the trustee in substantially the form reviewed by us;

(k)       to the extent that any opinion relates to the enforceability of the choice of New York law and choice of New York forum provisions contained in any Transaction Document, the opinions stated herein are subject to the qualification that such enforceability may be subject to, in each case, (i) the exceptions and limitations in New York General Obligations Law sections 5-1401 and 5-1402 and (ii) principles of comity and constitutionality; and

(l)        we do not express any opinion with respect to any laws, rules, regulations or orders concerning declared emergencies or the effect thereof on the opinions stated herein.

In addition, in rendering the foregoing opinions we have assumed that:

(a)        neither the execution and delivery by the Company of the Transaction Documents nor the performance by the Company of its obligations thereunder, including the issuance and sale of the applicable Securities: (i) constitutes or will constitute a violation of, or a default under, any lease, indenture, agreement or other instrument to which the Company or its property is subject, (ii) contravenes or will contravene any order or decree of any governmental authority to which the Company or its property is subject, or (iii) violates or will violate any law, rule or regulation to which the Company or its property is subject (except that we do not make the assumption set forth in this clause (iii) with respect to the Opined-on Law);

Applied Therapeutics, Inc.

June 12, 2020

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(b)       neither the execution and delivery by the Company of the Transaction Documents nor the performance by the Company of its obligations thereunder, including the issuance and sale of the applicable Securities, requires or will require the consent, approval, licensing or authorization of, or any filing, recording or registration with, any governmental authority under any law, rule or regulation of any jurisdiction; and

(c)        with respect to opinion paragraph 6 above, we have assumed that the issuance of the ATM Shares does not violate or conflict with any agreement or instrument binding on the Company (except that we do not make this assumption with respect to the Certificate of Incorporation, the Bylaws or those agreements or instruments expressed to be governed by the laws of the State of New York which are listed in Part II of the Registration Statement or the Company’s Annual Report on Form 10-K for the year ended December 31, 2019).

We hereby consent to the filing of this opinion with the Commission as an exhibit to the Registration Statement. We also hereby consent to the reference to our firm under the heading “Legal Matters” in the prospectus forming part of the Registration Statement. In giving this consent, we do not thereby admit that we are within the category of persons whose consent is required under Section 7 of the Securities Act or the Rules and Regulations. This opinion is expressed as of the date hereof unless otherwise expressly stated, and we disclaim any undertaking to advise you of any subsequent changes in the facts stated or assumed herein or of any subsequent changes in applicable laws.

Very truly yours,

/s/ SKADDEN, ARPS, SLATE, MEAGHER & FLOM LLP

MJS