Exhibit 5.1

+1 212 230 8800 (t)

+1 212 230 8888 (f)

wilmerhale.com

November 12, 2024

Climb Bio, Inc.

20 William Street, Suite 145

Wellesley Hills, Massachusetts 02481

Re: Registration Statement on Form S-3

Ladies and Gentlemen:

This opinion is furnished to you in connection with a Registration Statement on Form S-3 (the “Registration Statement”) to be filed by Climb Bio, Inc., a Delaware corporation (the “Company”), with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Securities Act”), for the registration of the following securities of the Company (the “Securities”):

i. senior debt securities (“Senior Debt Securities”);

ii. subordinated debt securities (“Subordinated Debt Securities” and, together with the Senior Debt Securities, “Debt Securities”);

iii. common stock, par value $0.0001 per share (“Common Stock”);

iv. preferred stock, par value $0.0001 per share (“Preferred Stock”);

v. subscription rights representing rights to purchase Debt Securities, Common Stock, Preferred Stock or other securities of the Company (“Subscription Rights”);

vi. warrants to purchase Debt Securities, Common Stock, Preferred Stock or other securities of the Company (“Warrants”); and

vii. units, consisting of one or more securities, including Debt Securities, Common Stock, Preferred Stock, Warrants or other securities of the Company (“Units”),

all of which may be issued from time to time on a delayed or continuous basis pursuant to Rule 415 under the Securities Act with an aggregate offering price of up to $200,000,000, as set forth in the Registration Statement, the base prospectus contained therein (the “Prospectus”) and any amendments or supplements thereto.

Climb Bio, Inc.
November 12, 2024
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We are acting as counsel for the Company in connection with the filing of the Registration Statement. The Senior Debt Securities may be issued pursuant to a senior indenture (the “Senior Indenture”) to be entered into between the Company and a trustee to be named, as trustee (the “Senior Trustee”) and duly qualified under the Trust Indenture Act of 1939, as amended (the “Trust Indenture Act”). The Subordinated Debt Securities may be issued pursuant to a subordinated indenture (the “Subordinated Indenture,” and, together with the Senior Indenture, the “Indentures,” and, each individually, an “Indenture”) to be entered into between the Company and a trustee to be named, as trustee (the “Subordinated Trustee” and, together with the Senior Trustee, the “Trustees,” and, each individually, a “Trustee”) and duly qualified under the Trust Indenture Act. The preferences, limitations and relative rights of shares of any series of Preferred Stock will be set forth in a Certificate of Designation (a “Certificate of Designation”). The Units may be issued pursuant to a Unit Agreement (the “Unit Agreement”) to be entered into between the Company and a bank or trust company to be named, as unit agent. The Subscription Rights may be issued pursuant to a subscription rights certificate or subscription rights agreement to be entered into between the Company and a bank or trust company to be named, as subscription agent (the “Subscription Rights Agreement”). The Warrants may be issued pursuant to a warrant agreement (the “Warrant Agreement”) to be entered into between the Company and a bank or trust company to be named, as warrant agent.

We have examined and relied upon signed copies of the Registration Statement to be filed with the Commission, including the exhibits thereto. We have also examined and relied upon the Amended and Restated Certificate of Incorporation of the Company (as amended or restated from time to time, the “Certificate of Incorporation”), the Amended and Restated Bylaws of the Company (as amended or restated from time to time, the “Bylaws”) and minutes of meetings of the stockholders and the Board of Directors of the Company, including duly authorized committees thereof as provided to us by the Company.

In our examination of the foregoing documents, we have assumed the genuineness of all signatures, the legal capacity of all signatories, the authenticity of all documents submitted to us as originals, the conformity to original documents of all documents submitted to us as copies, the authenticity of such original documents and the completeness and accuracy of the corporate minute books of the Company.

We have relied as to certain matters on information obtained from public officials and officers of the Company, and we have assumed (i) the Registration Statement will be effective and will comply with all applicable laws at the time Securities are offered or issued as contemplated by the Registration Statement; (ii) one or more prospectus supplements and term sheets, as applicable will have been prepared and filed with the Commission describing the Securities offered thereby; (iii) all Securities will be issued and sold in compliance with applicable federal and state securities laws and in the manner stated in the Registration Statement, the Prospectus and any applicable prospectus supplement; (iv) in the case of Debt Securities, (a) the applicable Indenture will be duly authorized, executed and delivered by the applicable Trustee in substantially the form filed as Exhibit 4.3 or Exhibit 4.4 to the Registration Statement, (b) the applicable Trustee will be duly eligible to serve as trustee, and (c) the Debt Securities will be duly authenticated by the Trustee named in the applicable Indenture; (v) any

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November 12, 2024
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Unit Agreement, Subscription Rights Agreement or Warrant Agreement, as applicable, will be duly authorized, executed and delivered by all parties thereto other than the Company; (vi) a definitive purchase, underwriting or similar agreement with respect to any Securities offered will be duly authorized, executed and delivered by all parties thereto other than the Company; (vii) any Securities issuable upon conversion, exchange or exercise of any Security being offered will be duly authorized, created and, if appropriate, reserved for issuance upon such conversion, exchange or exercise; (viii) with respect to shares of Common Stock or Preferred Stock offered, there will be sufficient shares of Common Stock or Preferred Stock authorized under the Certificate of Incorporation and not otherwise reserved for issuance; (ix) if issued in uncertificated form, valid book-entry notations for the issuance of the Common Stock or the Preferred Stock will have been duly made in the share register of the Company; (x) at the time of the issuance and sale of the Securities, the Company will be validly existing as a corporation and in good standing under the laws of the State of Delaware; and (xi) any Unit Agreement, Subscription Rights Agreement or Warrant Agreement will be governed by the laws of the State of New York or Delaware.

We are expressing no opinion herein as to the application of any federal or state law or regulation to the power, authority or competence of any party to any agreement with respect to any of the Securities other than the Company. We have assumed that such agreements are, or will be, the valid and binding obligations of each party thereto other than the Company, and enforceable against each such other party in accordance with their respective terms.

We have assumed for purposes of our opinions below that no authorization, approval or other action by, and no notice to or filing with, any governmental authority or regulatory body or any other third party is required for the due execution, delivery or performance by the Company, or, if any such authorization, approval, consent, action, notice or filing is required, it will have been duly obtained, taken, given or made and will be in full force and effect. We have also assumed that there will not have occurred, prior to the date of issuance of the Securities, any change in law affecting the validity or enforceability of such Securities and that at the time of the issuance and sale of such Securities, the Board of Directors of the Company (or any committee of such Board of Directors or any person acting pursuant to authority properly delegated to such person by the Board of Directors of the Company or any committee of such Board of Directors) shall not have taken any action to rescind or otherwise reduce its prior authorization of the issuance of such Securities.

Our opinions below are qualified to the extent that they may be subject to or affected by (i) applicable bankruptcy, insolvency, reorganization, receivership, moratorium, usury, fraudulent conveyance, fraudulent transfer or similar laws relating to or affecting the rights or remedies of creditors generally, (ii) duties and standards imposed on creditors and parties to contracts, including, without limitation, requirements of materiality, good faith, reasonableness and fair dealing, (iii) general equitable principles, and (iv) acceleration of the Debt Securities which may affect the collectability of that portion of the stated principal amount thereof that

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November 12, 2024
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might be determined to constitute unearned interest thereon. Furthermore, we express no opinion as to the availability of any equitable or specific remedy upon any breach of any of the agreements as to which we are opining herein, or any of the agreements, documents or obligations referred to therein, or to the successful assertion of any equitable defenses, inasmuch as the availability of such remedies or the success of any equitable defenses may be subject to the discretion of a court. We also express no opinion herein as to the laws of any state or jurisdiction other than the state laws of the State of New York and the General Corporation Law of the State of Delaware. We also express no opinion herein with respect to compliance by the Company with the securities or “blue sky” laws of any state or other jurisdiction of the United States or of any foreign jurisdiction. We express no opinion and make no statement herein with respect to the antifraud laws of any jurisdiction.

We also express no opinion herein as to any provision of any agreement (i) that may be deemed to or construed to waive any right, defense or counterclaim of the Company, (ii) to the effect that rights and remedies are not exclusive, that every right or remedy is cumulative and may be exercised in addition to or with any other right or remedy and does not preclude recourse to one or more other rights or remedies, (iii) relating to the effect of invalidity or unenforceability of any provision of any agreement on the validity or enforceability of any other provision thereof, (iv) that is in violation of public policy, (v) relating to indemnification and contribution with respect to securities law matters, (vi) that provides that the terms of any agreement may not be waived or modified except in writing, (vii) purporting to indemnify any person against his, her or its own negligence or intentional misconduct, (viii) requiring the payment of penalties, consequential damages or liquidated damages or limiting a party’s recovery of certain damages or losses, (ix) purporting to establish evidentiary standards or regarding standards for exercising rights and remedies or (x) relating to choice of law or consent to jurisdiction.

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

1. With respect to the Debt Securities, when (i) specifically authorized for issuance by proper action of the Board of Directors of the Company or an authorized committee thereof (the “Authorizing Resolutions”), (ii) the applicable Indenture has been duly authorized, executed and delivered by the Company, (iii) the terms of the Debt Securities and of their issuance and sale have been duly established in conformity with the applicable Indenture and the Authorizing Resolutions and assuming such terms and sale do not violate any applicable law or result in a default under or breach of any agreement or instrument binding upon the Company and comply with any requirement or restriction imposed by any court or governmental body having jurisdiction over the Company, (iv) such Debt Securities have been duly executed by the Company and authenticated by the applicable Trustee in accordance with the applicable Indenture and delivered and sold as contemplated by the Registration Statement, the Prospectus and any applicable prospectus supplement in accordance with the applicable underwriting or other purchase agreement against payment therefor, and (v) the Company has received the consideration provided for in the Authorizing Resolutions and the applicable underwriting agreement or other purchase agreement, such Debt Securities will constitute valid and binding obligations of the Company enforceable against the Company in accordance with their terms.

Climb Bio, Inc.
November 12, 2024
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2. With respect to shares of Common Stock, when (i) specifically authorized for issuance by Authorizing Resolutions, (ii) the terms of the issuance and sale of the Common Stock have been duly established in conformity with the Certificate of Incorporation, Bylaws and Authorizing Resolutions, (iii) the shares of Common Stock have been issued and delivered as contemplated by the Registration Statement, the Prospectus and any applicable prospectus supplement in accordance with the applicable underwriting or other purchase agreement or upon conversion or exercise of any Security offered under the Registration Statement against payment therefor, and (iv) the Company has received the consideration provided for in the Authorizing Resolutions and the applicable underwriting agreement or other purchase agreement and such consideration per share is not less than the par value per share of the Common Stock, the Common Stock will be validly issued, fully paid and non-assessable.

3. With respect to shares of any series of Preferred Stock, when (i) the Authorizing Resolutions have specifically authorized the issuance and terms of the shares of the series, the terms of the offering thereof and related matters, including resolutions establishing and designating the series and fixing and determining the preferences, limitations and relative rights thereof and the filing of a Certificate of Designation with respect to the series with the Secretary of State of the State of Delaware, and such Certificate of Designation has been duly filed, (ii) the terms of the issuance and sale of the series of Preferred Stock have been duly established in conformity with the Certificate of Incorporation, Bylaws and Authorizing Resolutions, (iii) the shares of the series of Preferred Stock have been issued and delivered as contemplated by the Registration Statement, the Prospectus and any applicable prospectus supplement in accordance with the applicable underwriting or other purchase agreement against payment therefor, and (iv) the Company has received the consideration provided for in the Authorizing Resolutions and the applicable underwriting agreement or other purchase agreement and such consideration per share is not less than the par value per share of the Preferred Stock, the shares of such series of Preferred Stock will be validly issued, fully paid and non-assessable.

4. With respect to the Units, when (i) specifically authorized for issuance by Authorizing Resolutions, (ii) any applicable Unit Agreement has been duly authorized, executed and delivered, (iii) the terms of the Units and of their issuance and sale have been duly established in conformity with any applicable Unit Agreement and the Authorizing Resolutions, (iv) the Units have been duly executed and delivered in accordance with any applicable Unit Agreement and issued and delivered as contemplated by the Registration Statement, the Prospectus and any applicable prospectus supplement in accordance with the applicable underwriting or other purchase agreement against payment therefor, and (v) the Company has received the consideration provided for in the Authorizing Resolutions and the applicable underwriting agreement or other purchase agreement, such Units will constitute valid and binding obligations of the Company enforceable against the Company in accordance with their terms.

Climb Bio, Inc.
November 12, 2024
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5. With respect to the Subscription Rights, when (i) specifically authorized for issuance by Authorizing Resolutions, (ii) any applicable Subscription Rights Agreement has been duly authorized, executed and delivered, (iii) the terms of the Subscription Rights and of their issuance and sale have been duly established in conformity with any applicable Subscription Rights Agreement and the Authorizing Resolutions, (iv) the Subscription Rights have been duly executed and delivered in accordance with any applicable Subscription Rights Agreement and issued and delivered as contemplated by the Registration Statement, the Prospectus and any applicable prospectus supplement in accordance with the applicable underwriting or other purchase agreement against payment therefor, and (v) the Company has received the consideration provided for in the Authorizing Resolutions and the applicable underwriting agreement or other purchase agreement, such Subscription Rights will constitute valid and binding obligations of the Company enforceable against the Company in accordance with their terms.

6. With respect to the Warrants, when (i) specifically authorized for issuance by the Authorizing Resolutions, (ii) any applicable Warrant Agreement relating to the Warrants has been duly authorized, executed and delivered by the Company, (iii) the terms of the Warrants and of their issuance and sale have been duly established in conformity with any applicable Warrant Agreement and the Authorizing Resolutions, (iv) the Warrants have been duly executed by the Company and countersigned in accordance with any Warrant Agreement and Authorizing Resolutions and issued and delivered as contemplated by the Registration Statement, the Prospectus and any applicable prospectus supplement in accordance with the applicable underwriting or other purchase agreement against payment therefor, and (v) the Company has received the consideration provided for in the Authorizing Resolutions and the applicable underwriting agreement or other purchase agreement, such Warrants will constitute valid and binding obligations of the Company enforceable against the Company in accordance with their terms.

Please note that we are opining only as to the matters expressly set forth herein, and no opinion should be inferred as to any other matters. This opinion is based upon currently existing statutes, rules, regulations and judicial decisions, and we disclaim any obligation to advise you of any change in any of these sources of law or subsequent legal or factual developments which might affect any matters or opinions set forth herein.

We hereby consent to the filing of this opinion with the Commission 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 and to the use of our name therein and in the related Prospectus and in any prospectus supplement under the caption “Legal Matters.” 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.

Climb Bio, Inc.
November 12, 2024
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Very truly yours,

/s/ Wilmer Cutler Pickering Hale and Dorr LLP

WILMER CUTLER PICKERING HALE AND DORR LLP