Exhibit 5.1

January 6, 2015

Board of Directors

Five Prime Therapeutics, Inc.

Two Corporate Drive

South San Francisco, CA 94080

Gentlemen:

We are acting as counsel to Five Prime Therapeutics, Inc., a Delaware corporation (the “Company”), in connection with its registration statement on Form S-3, as amended (the “Registration Statement”), filed with the Securities and Exchange Commission relating to the proposed public offering of up to 3,921,500 in aggregate amount of shares of the Company’s common stock, $0.001 par value per share (the “Common Shares”), all of which may be sold from time to time and on a delayed or continuous basis, as set forth in the prospectus which forms a part of the Registration Statement, and as to be set forth in one or more supplements to the prospectus.

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.

For purposes of this opinion letter, we have examined copies of such agreements, instruments and documents as we have deemed an appropriate basis on which to render the opinions hereinafter expressed. In our examination of the aforesaid documents, we have assumed the genuineness of all signatures, the legal capacity of all natural persons, the accuracy and completeness of all documents submitted to us, the authenticity of all original documents, and the conformity to authentic original documents of all documents submitted to us as copies (including telecopies). As to all matters of fact, we have relied on the representations and statements of fact made in the documents so reviewed, and we have not independently established the facts so relied on. This opinion letter is given, and all statements herein are made, in the context of the foregoing.

For purposes of this opinion letter, we have assumed that (i) the issuance, sale, amount and terms of any Common Shares of the Company to be offered from time to time will have been duly authorized and established by proper action of the board of directors of the Company or a duly authorized committee of such board (“Board Action”) consistent with the procedures and terms described in the Registration Statement and in accordance with the Company’s charter and bylaws and applicable Delaware corporate law, in a manner that does not violate any law, government or court-imposed order or restriction or agreement or instrument then binding on the Company or otherwise impair the legal or binding nature of the obligations represented by the applicable Securities; (ii) at the time of offer, issuance and sale of any Common Shares, the Registration Statement will have been declared effective under the Securities Act of 1933, as amended (the “Act”), and no stop order suspending its effectiveness will have been issued and remain in effect; (iii) if being sold by the issuer thereof, the Common Shares will be delivered against payment of valid consideration therefor and in accordance with the terms of the applicable Board Action authorizing such sale and any applicable

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underwriting agreement or purchase agreement and as contemplated by the Registration Statement and/or the applicable prospectus supplement; and (iv) the Company will remain a Delaware corporation.

This opinion letter is based as to matters of law solely on the applicable provisions, as currently in effect, of the Delaware General Corporation Law, as amended. We express no opinion herein as to any other laws, statutes, ordinances, rules, or regulations (and in particular, we express no opinion as to any effect that such other laws, statutes, ordinances, rules, or regulations may have on the opinions expressed herein).

Based upon, subject to and limited by the foregoing, we are of the opinion that the Common Shares, upon due execution and delivery on behalf of the Company of certificates therefor, including global certificates, or the entry of the issuance thereof in the books and records of the Company, as the case may be, will be validly issued, fully paid and nonassessable.

This opinion letter has been prepared for use in connection with the Registration Statement. We assume no obligation to advise you of any changes in the foregoing subsequent to the effective date of the Registration Statement.

We hereby consent to the filing of this opinion letter as Exhibit 5.1 to the Registration Statement and to the reference to this firm under the caption “Legal Matters” in the prospectus constituting a part of the Registration Statement. In giving this consent, we do not thereby admit that we are an “expert” within the meaning of the Securities Act of 1933, as amended.

Very truly yours,

/s/ HOGAN LOVELLS US LLP

HOGAN LOVELLS US LLP