Exhibit 5.1

Charles J. Bair

+1 858 550 6142

cbair@cooley.com

May 19, 2020

Turning Point Therapeutics, Inc.

10628 Science Center Drive, Ste. 200

San Diego, CA 92121

Ladies and Gentlemen:

We have acted as counsel to Turning Point Therapeutics, Inc., a Delaware corporation (the “Company”), in connection with the offering by the Company of up to 6,229,167 shares of the Company’s common stock, par value $0.0001 (the “Shares”), including up to 812,500 Shares that may be sold pursuant to the exercise of an option to purchase additional shares, pursuant to a Registration Statement on Form S-3ASR (Registration Statement No.333-238300) (the “Registration Statement”), filed with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Act”), the base prospectus included in the Registration Statement (the “Base Prospectus”), and the prospectus supplement relating to the Shares filed with the Commission pursuant to Rule 424(b) of the Rules and Regulations of the Act (together with the Base Prospectus, the “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, each as currently in effect, and 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. We have assumed the genuineness of all documents submitted to us as originals, the conformity to originals of all documents submitted to us as copies, the accuracy, completeness and authenticity of certificates of public officials and the due execution and delivery of documents by all persons other than the Company where execution and delivery are prerequisites to the effectiveness thereof. As to certain factual matters, we have relied upon a certificate of an officer of the Company and have not independently verified such matters.

Our opinion is expressed only with respect to the General Corporation Law of the State of Delaware. We express no opinion to the extent that any other laws are applicable to the subject matter hereof and express no opinion and provide no assurance as to compliance with any federal or state securities law, rule or regulation.

On the basis of the foregoing, and in reliance thereon, we are of the opinion that the Shares, when sold in accordance with the Registration Statement and the Prospectus, will be validly issued, fully paid and nonassessable.

Cooley LLP 4401 Eastgate Mall San Diego, CA 92121

t: (858) 550-6000 f: (858) 550-6420 cooley.com

Turning Point Therapeutics, Inc.

May 19, 2020

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 in the Registration Statement.

Sincerely,

Cooley LLP 4401 Eastgate Mall San Diego, CA 92121

t: (858) 550-6000 f: (858) 550-6420 cooley.com