Exhibit 5.1

Charles J. Bair

+1 858 550 6142

cbair@cooley.com

March 12, 2018

Kura Oncology, Inc.

3033 Science Park Road, Suite 220

San Diego, CA 92121

Ladies and Gentlemen:

You have requested our opinion, as counsel to Kura Oncology, Inc., a Delaware corporation (the “Company”), with respect to certain matters in connection with the offering by the Company of the lesser of (i) $60,000,000 of shares or (ii) 60,000,000 shares of the Company’s common stock, par value $0.0001 (the “Shares”), pursuant to a Registration Statement on Form S-3 (No. 333-221479) (the “Registration Statement”), filed with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Act”), the prospectus included within the Registration Statement (the “Base Prospectus”), and the prospectus supplement dated March 12, 2018, filed with the Commission pursuant to Rule 424(b) of the Rules and Regulations of the Act (the “Prospectus Supplement” and together with the Base Prospectus, the “Prospectus”). The Shares are to be sold by the Company in accordance with the Amended and Restated Sales Agreement, dated March 12, 2018, between the Company and Cowen and Company, LLC (the “Agreement”), as described in the Prospectus.

In connection with this opinion, we have examined and relied upon the Registration Statement and the Prospectus, the Agreement, the Company’s Amended and Restated Certificate of Incorporation, as amended, its Amended and Restated Bylaws, and the originals or copies certified to our satisfaction of such records, documents, certificates, memoranda and other instruments as in our judgment are necessary or appropriate to enable us to render the opinion expressed below. In rendering this opinion, we have assumed the genuineness and authenticity of all signatures on original documents; the genuineness and authenticity of all documents submitted to us as originals; the conformity to originals of all documents submitted to us as copies; and the accuracy, completeness and authenticity of certificates of public officials.

Our opinion herein is expressed solely with respect to the federal laws of the United States of America and the General Corporation Law of the State of Delaware. Our opinion is based on these laws as in effect on the date hereof. We express no opinion as to whether the laws of any particular jurisdiction other than those identified above are applicable to the subject matter hereof.

On the basis of the foregoing, and in reliance thereon, we are of the opinion that the Shares, when sold and issued against payment therefor in accordance with the Agreement, the Registration Statement and the Prospectus, will be validly issued, fully paid and nonassessable, subject to obtaining the approval of the specific issuance of the Shares by the Board of Directors of the Company or a duly authorized committee thereof.

COOLEY LLP 4401 EASTGATE MALL SAN DIEGO, CA 92121

T: (858) 550-6000 F: (858) 550-6420 COOLEY.COM

Kura Oncology, Inc.

March 12, 2018

Page Two

We consent to the reference to our firm under the caption “Legal Matters” in the Prospectus and to the filing of this opinion as an exhibit to a Current Report on Form 8-K to be filed with the Commission for incorporation by reference into the Registration Statement.

Sincerely,

COOLEY LLP 4401 EASTGATE MALL SAN DIEGO, CA 92121

T: (858) 550-6000 F: (858) 550-6420 COOLEY.COM