Exhibit 5.1

March 5, 2026

Contineum Therapeutics, Inc.

3565 General Atomics Court, Suite 200

San Diego, CA 92121

Ladies and Gentlemen:

We have acted as counsel to Contineum Therapeutics, Inc., a Delaware corporation (the “Company”), and you have requested our opinion with respect to certain matters in connection with the offering by the Company of the number of authorized but unissued shares having aggregate sale proceeds of up to $100 million (the “Shares”) of the Company’s Class A common stock, par value $0.001 per share (the “Common Stock”), to be issued pursuant to (i) the Registration Statement on Form S-3 (File No. 333-287275) filed on May 14, 2025 with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Act”), which was declared effective by the Commission on May 23, 2025 (the “Registration Statement”), the related prospectus, included in the Registration Statement (the “Base Prospectus”), and the related at-the-market offering prospectus supplement, dated March 5, 2026, to be filed with the Commission pursuant to Rule 424(b) under the Act (the “ATM Prospectus”), and (ii) that certain Sales Agreement, dated May 14, 2025, by and between the Company and Leerink Partners LLC, as amended by Amendment No. 1, dated March 5, 2026, by and between the Company and Leerink Partners LLC (the “Sale Agreement”). The Base Prospectus and the ATM Prospectus are collectively referred to as the “Prospectus.” The Shares are to be sold by the Company in accordance with the Sale Agreement, as described in the ATM Prospectus.

In connection with this opinion, we have examined and relied upon the Registration Statement, the Prospectus, the Company’s Amended and Restated Certificate of Incorporation and Amended and Restated Bylaws, as currently in effect, and the originals or copies certified to our satisfaction of such other documents, records, certificates, memoranda and other instruments as in our judgment are necessary or appropriate to enable us to render the opinion expressed below. With your consent, we have relied upon certificates and other assurances of officers of the Company as to factual matters without having independently verified such factual matters. We have assumed the genuineness and authenticity of all documents submitted to us as originals, and the conformity to originals of all documents submitted to us as copies thereof and the due execution and delivery by all parties other than the Company of all documents where due execution and delivery are a prerequisite to the effectiveness thereof.

This opinion is being furnished in connection with the requirements of Item 601(b)(5) of Regulation S-K under the Act, and no opinion is expressed herein as to any matter pertaining to the contents of the Registration Statement or the Prospectus, other than as expressly stated herein with respect to the issue of the Shares. Our opinion is limited to the matters stated herein and no opinion is implied or may be inferred beyond the matters expressly stated. Our opinion herein is expressed solely with respect to the General Corporation Law of the State of Delaware and we express no opinion with respect to any other laws. Our opinion is based on these laws as in effect on the date hereof, and we disclaim any obligation to advise you of facts, circumstances, events or developments which hereafter may be brought to our attention and which may alter, affect or modify the opinion expressed herein.

Subject to the foregoing and the other matters set forth herein, it is our opinion that, when the Shares to be issued and sold by the Company are issued and paid for in accordance with the terms of the Sale Agreement, such Shares will be validly issued, fully paid and nonassessable.

We consent to the reference to our firm under the caption “Legal Matters” in the ATM Prospectus and to the filing of this opinion as an exhibit to the Company’s Current Report on Form 8-K to be filed with the Commission on March 5, 2026. In giving such consent, we do not thereby admit that we are in the category of persons whose consent is required under Section 7 of the Act or the rules and regulations of the Commission thereunder.

Very truly yours,

/s/ Gunderson Dettmer Stough Villeneuve Franklin & Hachigian, LLP

GUNDERSON DETTMER STOUGH VILLENEUVE FRANKLIN & HACHIGIAN, LLP

Contineum Therapeutics, Inc. 8-K