Exhibit 5.1

Sheppard, Mullin, Richter & Hampton LLP 30 Rockefeller Plaza New York, New York 10112-0015 212.653.8700 main 212.653.8701 fax www.sheppardmullin.com

December 15, 2020

VIA ELECTRONIC MAIL

Greenwich LifeSciences, Inc.

3992 Bluebonnet Dr, Building 14

Stafford, TX 77477

Re: Registration Statement on Form S-1

Ladies and Gentlemen:

We are acting as counsel to Greenwich LifeSciences, Inc., a Delaware corporation (the “Company”), in connection with its registration statement on Form S-1 (the “Registration Statement”), filed with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Act”), relating to the proposed public offering of shares of common stock of the Company, par value $0.001 per share (the “Shares”), with a proposed maximum aggregate offering price of $25.3 million, including Shares issuable upon exercise of an option granted by the Company. The Shares will be sold by the Company pursuant to an underwriting agreement to be entered into by and between the Company and Aegis Capital Corp. as the representative of the several underwriters to be named therein (the “Agreement”). This opinion letter is furnished to you at your request to enable you to fulfill the requirements of Item 601(b)(5) of Regulation S-K, 17 C.F.R. §229.601(b)(5), in connection with the Registration Statement.

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, subject to and limited by the foregoing, we are of the opinion that following (i) execution and delivery by the Company of the Agreement, (ii) effectiveness of the Registration Statement, (iii) issuance of the Shares pursuant to the terms of the Agreement, and (iv) receipt by the Company of the consideration for the Shares specified in the resolutions, the Shares will be duly authorized for issuance and, when issued, delivered and paid for in accordance with the terms of the Agreement, will be validly issued, fully paid and nonassessable.

We also hereby consent to the reference to our firm under the caption “Legal Matters” in the prospectus which forms part of the Registration Statement. 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 Act, the rules and regulations of the Commission promulgated thereunder or Item 509 of Regulation S-K.

Sheppard, Mullin, Richter & Hampton LLP 30 Rockefeller Plaza New York, New York 10112-0015 212.653.8700 main 212.653.8701 fax www.sheppardmullin.com

We express no opinion as to matters governed by any laws other than the Delaware General Corporation Law. No opinion is expressed herein with respect to the qualification of the Shares under the securities or blue sky laws of any state or any foreign jurisdiction.

This opinion letter is rendered to you solely for use in connection with the issuance and sale of the Shares in accordance with the Registration Statement as of the date first written above and is not to be relied on for any other purpose. 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.