Exhibit 5.1

Sheppard, Mullin, Richter & Hampton LLP 30 Rockefeller Plaza New York, NY 10112 T: +1.212.653.8700 | F: +1.212.653.8701 sheppard.com

February 20, 2026

VIA ELECTRONIC MAIL

TriSalus Life Sciences, Inc.

6272 W 91^st Ave.

Westminster, CO 80031

Ladies and Gentlemen:

We have acted as counsel to TriSalus Life Sciences, Inc., a Delaware corporation (the “Company”), in connection with the issuance and sale of up to 11,219,515 shares (including up to 1,463,415 shares issuable upon exercise of the underwriters’ option to purchase additional shares) of common stock of the Company, par value $0.0001 per share (the “Shares”). The offering of the Shares was made pursuant to a registration statement on Form S-3 under the Securities Act of 1933, as amended (the “Securities Act”), filed with the Securities and Exchange Commission (the “Commission”) on November 13, 2025 (File No. 333-291509) (the “Registration Statement”). The Shares are being sold pursuant to an underwriting agreement dated February 19, 2026 by and between the Company and Lake Street Capital Markets, LLC, as representative (the “Representative”) of the several underwriters named therein (the “Underwriting Agreement”).

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

In connection with this opinion, we have reviewed and relied upon the following:

In our examination, we have assumed the genuineness of all signatures, including endorsements, 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 photocopy, 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.

Based upon the foregoing and subject to the qualifications and assumptions stated herein, we are of the opinion that the Shares have been duly authorized by all requisite corporate action on the part of the Company under the Delaware General Corporation Law (the “DGCL”) and, when the Shares are delivered to and paid for by the Representative in accordance with the terms of the Underwriting Agreement and when evidence of the issuance thereof is duly recorded in the Company’s books and records, the Shares will be validly issued, fully paid and non-assessable.

We hereby consent to the filing of this opinion letter as an exhibit to the Company’s Current Report on Form 8-K being filed on the date hereof and incorporated by reference into the Registration Statement. We also hereby consent to the reference to our firm under the caption “Legal Matters” in the Prospectus. In giving this consent, we do not admit that we are within the category of persons whose consent is required under Section 7 of the Securities Act, the rules and regulations of the Commission promulgated thereunder or Item 509 of Regulation S-K.

We express no opinion as to matters governed by any laws other than the DGCL.

We disclaim any obligation to advise you of facts, circumstances, events or developments that hereafter may be brought to our attention and that may alter, affect or modify the opinion expressed herein. Our opinion is expressly limited to the matters set forth above and we render no opinion, whether by implication or otherwise, as to any other matters relating to the Company or the Shares.