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Exhibit 5.1

Madison A. Jones

+1 202 728 7087

madison.jones@cooley.com

May 30, 2025

Tvardi Therapeutics, Inc.

3 Sugar Creek Ctr. Blvd.

Suite 525

Sugar Land, TX 77478

Ladies and Gentlemen:

We have acted as counsel to Tvardi Therapeutics, Inc., a Delaware corporation (the “Company”) (f/k/a Cara Therapeutics, Inc.), in connection with the filing by the Company of a Registration Statement on Form S-1 (the “Registration Statement”) with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Securities Act”), including a related prospectus included in the Registration Statement (the “Prospectus”), covering the registration for resale of up to 2,084,117 shares (the “Shares”) of the Company’s common stock, $0.001 par value per share.  The Shares were issued pursuant to the Agreement and Plan of Merger and Reorganization, dated as of December 17, 2024 (the “Merger Agreement”), by and among the Company, CT Convergence Merger Sub, and Tvardi Operating Company, Inc. (f/k/a Tvardi Therapeutics, Inc.).

In connection with this opinion, we have examined and relied upon the Registration Statement, the Prospectus, the Merger Agreement, the Company’s certificate of incorporation and bylaws, each as currently in effect, and such other records, documents, opinions, certificates, memoranda and instruments as in our judgment are necessary or appropriate to enable us to render the opinion expressed below.  We have assumed the genuineness of all signatures, the authenticity of all documents submitted to us as originals, the conformity to originals of all documents submitted to us as copies, the accuracy, completeness and authenticity of certificates of public officials and the due authorization, execution and delivery of all documents by all persons other than the Company.  As to certain factual matters, we have relied upon a certificate of an officer of the Company and have not independently verified such matters.

Our opinion is expressed only with respect to the General Corporation Law of the State of Delaware.  We express no opinion to the extent that any other laws are applicable to the subject matter hereof and express no opinion and provide no assurance as to compliance with any federal or state securities law, rule or regulation.

On the basis of the foregoing, and in reliance thereon, we are of the opinion that the Shares are validly issued, fully paid and nonassessable.

Our opinion is limited to the matters expressly set forth in this letter, and no opinion has been or should be implied, or may be inferred, beyond the matters expressly stated. This opinion speaks only as to law and facts in effect or existing as of the date hereof, and we have no obligation or responsibility to update or supplement this letter to reflect any facts or circumstances that may hereafter come to our attention or any changes in law that may hereafter occur.

Cooley LLP 1299 Pennsylvania Avenue, NW, Suite 700 Washington, DC 20004-2400
t: (202) 842-7800 f: (202) 842-7899 cooley.com


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Tvardi Therapeutics, Inc.

May 30, 2025

Page Two

We hereby consent to the reference to our firm under the heading “Legal Matters” in the Prospectus and to the filing of this opinion as an exhibit to the Registration Statement.  In giving such consents, we do not thereby 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 thereunder.

Very truly yours,

Cooley LLP

By:

/s/ Madison A. Jones

     Madison A. Jones

Cooley LLP 1299 Pennsylvania Avenue, NW, Suite 700 Washington, DC 20004-2400
t: (202) 842-7800 f: (202) 842-7899 cooley.com