Exhibit 5.1

June 6, 2024

Shake Shack Inc.

225 Varick Street, Suite 301

New York, NY 10014

Ladies and Gentlemen:

We have acted as special counsel for Shake Shack Inc., a Delaware corporation (the “Company”), in connection with the preparation of the Registration Statement on Form S-3 (the “Registration Statement”) filed on or about the date hereof with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Securities Act”). The Registration Statement contains a prospectus (the “Base Prospectus”) that provides it will be supplemented in the future by one or more prospectus supplements, and a resale prospectus (the “Resale Prospectus”), and relates to:

(a) The Company’s offer and sale from time to time, pursuant to Rule 415 promulgated under the Securities Act, of an undetermined amount of the following securities:

i) debt securities (the “Debt Securities”);

ii) shares (“Company Shares”) of Class A common stock, $0.001 par value per share, of the Company (“Class A Common Stock”);

iii) shares of preferred stock, $0.001 par value per share, of the Company (the “Preferred Stock”);

iv) warrants to purchase Debt Securities, Class A Common Stock, or Preferred Stock evidenced by warrant certificates independently or together with any securities offered by a prospectus supplement (the “Warrants”);

v) rights to purchase Class A Common Stock or Preferred Stock (the “Rights”);

vi) depositary shares representing Preferred Stock (the “Depositary Shares”); and

vii) units of a combination of one or more of the securities described in clauses (i) through (vi) above (the “Units” and together with the Debt Securities, Company Shares, Preferred Stock, Warrants, Rights, and Depositary Shares, the “Company Securities”).

(b) The proposed resale of up to 5,626,015 shares of Class A Common Stock (the “Selling Stockholder Shares” and, together with the Company Securities, the “Securities”). The Selling Stockholder Shares are to be offered and sold by the selling stockholders listed in the Resale Prospectus (the “Selling Stockholders”), and consist of (i) 3,138,079 shares of Class A Common Stock (“Current Shares”) that have been issued to certain of the Selling Stockholders, and (ii) 2,487,936 shares of Class A Common Stock (“Redemption Shares”) that may be issued by the Company upon the redemption (or exchange) by certain of the Selling Stockholders of an equivalent number of LLC interests of SSE Holdings, LLC.

We have examined: (i) the Registration Statement; (ii) the Base Prospectus; (iii) the Resale Prospectus; (iv) the amended and restated bylaws of the Company, as amended and currently in effect; (v) the Certificate of Incorporation of the Company, as amended and restated; (vi) the Limited Liability Company Agreement of SSE Holdings, LLC, as amended (the “LLC Agreement”); (vii) the form of indenture filed as an exhibit to the Registration Statement; and (viii) such other documents as we have deemed necessary or appropriate for purposes of this opinion.

In connection with this opinion, we have assumed that:

a) any Debt Securities will be issued pursuant to one or more indentures, each to be between the Company and a financial institution identified therein as trustee;

b) prior to the delivery of any Company Security, the Board of Directors shall have duly established the terms of such Security and duly authorized the issuance and sale of such Security and such authorization shall not have been modified or rescinded;

c) the Registration Statement, and any amendments thereto (including post-effective amendments), will have become effective and such effectiveness shall not have been terminated or rescinded;

d) a prospectus supplement will have been prepared and filed with the Commission describing the Company Securities offered thereby;

e) all Company Securities will be issued and sold in compliance with applicable federal and state securities laws and in the manner stated in the Registration Statement and the appropriate prospectus supplement;

f) a definitive purchase, underwriting or similar agreement with respect to any Company Securities will have been duly authorized and validly executed and delivered by the Company and the other parties thereto;

g) there shall be no change in law affecting the validity of any of the Securities (between the date hereof and the date of issuance and sale of such Securities); and

h) all parties to agreements involving the issuance or sale of the Securities will perform their obligations thereunder in compliance with the terms of such documents.

Based upon and subject to the foregoing, we are of the opinion that,

(1) With respect to the Debt Securities, when (i) an indenture relating thereto has been duly qualified under the Trust Indenture Act of 1939, as amended; (ii) the Board (or a duly constituted and acting committee thereof) has taken all necessary action to approve the issuance of the Debt Securities, the terms of the offering thereof and related matters; and (iii) the Debt Securities have been duly executed, authenticated, issued and delivered in accordance with the terms of the indenture and the applicable definitive purchase, underwriting or similar agreement approved by the Company, and upon payment of the consideration therefor or provided for therein, then the Debt Securities will constitute legal, valid and binding obligations of the Company, enforceable against the Company in accordance with their terms, except as such enforcement may be subject to any applicable bankruptcy, insolvency, reorganization, fraudulent conveyance or other law relating to or affecting creditors’ rights generally and general principles of equity.

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(2) With respect to the Company Shares, when (i) the Board (or a duly constituted and acting committee thereof) has taken all necessary action to approve the issuance and sale of the Company Shares, the terms of the offering thereof and related matters, (ii) such Company Shares have been issued and delivered in accordance with the provisions of any applicable convertible or exchangeable security, definitive purchase, underwriting or other agreement binding on the Company and the terms approved by the Board (or a duly constituted and acting committee thereof) and (iii) the Company has received payment of the cash or other lawful consideration provided to be paid for the Company Shares, which consideration shall not be less than the par value thereof, such Company Shares will be legally issued, fully paid and non-assessable.

(3) With respect to the Preferred Stock, when (i) the Board (or a duly constituted and acting committee thereof) has taken all necessary action to approve the designation of the relative rights, preferences and limitations of any series of Preferred Stock, (ii) a Certificate of Designations relating to such series of Preferred Stock has been properly filed with the Secretary of State of the State of Delaware, (iii) the Board (or a duly constituted and acting committee thereof) has taken all necessary action to approve the issuance and sale of such shares of Preferred Stock, the terms of the offering thereof and related matters, (iv) such shares of Preferred Stock have been issued and delivered in accordance with the provisions of any applicable convertible or exchangeable security, definitive purchase, underwriting or other agreement binding on the Company and the terms approved by the Board (or a duly constituted and acting committee thereof) and (v) the Company has received payment of the cash or other lawful consideration provided to be paid for the Preferred Stock, which consideration shall not be less than the par value thereof, such shares of Preferred Stock will be legally issued, fully paid and non-assessable.

(4) With respect to the Warrants, when (i) the Board (or a duly constituted and acting committee thereof) has taken all necessary action to approve the issuance and establish the terms of the Warrants, the terms of the offering of such Warrants, and related matters, (ii) one or more agreements incorporating the terms and other provisions of the Warrants has been duly executed and delivered by the Company and a warrant agent (each, a “Warrant Agreement”), (iii) the Warrant certificates have been duly executed, authenticated or countersigned, issued and delivered in accordance with the terms of the appropriate Warrant Agreement (assuming the Securities issuable upon exercise of the Warrants have been duly authorized and reserved for issuance by all necessary corporate action), and upon payment of the consideration therefor or provided for therein, then the Warrants will constitute legal, valid and binding obligations of the Company, enforceable against the Company in accordance with their terms, except as such enforcement may be subject to any applicable bankruptcy, insolvency, reorganization, fraudulent conveyance or other law relating to or affecting creditors’ rights generally and general principles of equity.

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(5) With respect to the Rights, when (i) the Board (or a duly constituted and acting committee thereof) has taken all necessary action to approve the issuance and establish the terms of the Rights, the terms of the offering of such Rights, and related matters, (ii) one or more agreements incorporating the terms and other provisions of the Rights has been duly executed and delivered by the Company (each, a “Rights Agreement”), (iii) the Rights have been duly executed, authenticated, issued and delivered in accordance with the applicable Rights Agreement (assuming the Common Stock and Preferred Stock issuable upon exercise of the Rights have been duly authorized and reserved for issuance by all necessary corporate action), and upon payment of the consideration therefor or provided for therein, then the Rights will constitute legal, valid and binding obligations of the Company, enforceable against the Company in accordance with their terms, except as such enforcement may be subject to any applicable bankruptcy, insolvency, reorganization, fraudulent conveyance or other law relating to or affecting creditors’ rights generally and general principles of equity.

(6) With respect to the Depositary Shares, when (i) the Board (or a duly constituted and acting committee thereof) has taken all necessary action to approve the issuance and establish the terms of the Depositary Shares, the terms of the offering of such Depositary Shares, and related matters, (ii) one or more agreements incorporating the terms and other provisions of the Depositary Shares has been executed and delivered by the Company (each, a “Deposit Agreement”), (iii) the depositary receipts evidencing the Depositary Shares have been duly executed, authenticated, issued and delivered by the depositary in accordance with the applicable Deposit Agreement (assuming the Preferred Stock issuable upon exercise of the Depositary Shares have been duly authorized and reserved for issuance by all necessary corporate action), and upon payment of the consideration therefor or provided for therein, then the Depositary Shares will constitute legal, valid and binding obligations of the Company, enforceable against the Company in accordance with their terms, except as such enforcement may be subject to any applicable bankruptcy, insolvency, reorganization, fraudulent conveyance or other law relating to or affecting creditors’ rights generally and general principles of equity.

(7) With respect to the Units, when (i) the Board (or a duly constituted and acting committee thereof) has taken all necessary action to approve the issuance and establish the terms of the Units, the terms of the offering of such Units, and related matters, (ii) one or more agreements incorporating the terms and other provisions thereof has been duly executed and delivered by the Company and a unit agent (each, a “Unit Agreement”), (iii) the Unit certificates have been duly executed, authenticated or countersigned, issued and delivered in accordance with the terms of the appropriate Unit Agreement (assuming the Securities issuable upon exercise of the Securities comprising the Units have been duly authorized and reserved for issuance by all necessary corporate action), and upon payment of the consideration therefor or provided for therein, then the Units will constitute legal, valid and binding obligations of the Company, enforceable against the Company in accordance with their terms, except as such enforcement may be subject to any applicable bankruptcy, insolvency, reorganization, fraudulent conveyance or other law relating to or affecting creditors’ rights generally and general principles of equity.

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(8) The Current Shares have been duly authorized by the Company and are legally issued, fully paid and non-assessable.

(9) When the Redemption Shares shall have been duly registered on the books of the transfer agent and registrar therefor in the name or on behalf of the Selling Stockholders, and have been issued by the Company against the consideration therefor contemplated by the LLC Agreement, the Redemption Shares will have been duly authorized, legally issued, fully paid and non-assessable.

The opinions expressed herein are qualified in the following respects:

(1) We have assumed that (i) each document submitted to us for review is accurate and complete, each such document that is an original is authentic, each such document that is a copy conforms to an authentic original and all signatures on each such document are genuine and (ii) each certificate from governmental officials reviewed by us is accurate, complete and authentic, and all official public records are accurate and complete.

(2) This opinion is limited in all respects to the laws of the State of New York and the General Corporation Law of the State of Delaware.

We hereby consent to the references to this firm under the caption “Legal Matters” in the Base Prospectus and the Resale Prospectus contained in the Registration Statement and to the filing of this opinion as an exhibit to the Registration Statement in accordance with the requirements of Item 601(b)(5) of Regulation S-K under the Securities Act. In giving such consent, we do not hereby admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the Commission.

Very truly yours,

/s/ Proskauer Rose LLP

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