Exhibit 5.1

Divakar Gupta
T: +1 212 479 6474
dgupta@cooley.com
May 20, 2019
Applied Therapeutics, Inc.
340 Madison Avenue, 19th Floor
New York, New York 10173
Re: Registration on Form S-8
Ladies and Gentlemen:
We have acted as counsel to Applied Therapeutics, Inc., a Delaware corporation (the “Company”), and you have requested our opinion in connection with the filing of a registration statement on Form S-8 (the “Registration Statement”) with the Securities and Exchange Commission, covering the offering of up to 4,710,000 shares of the Company’s Common Stock, par value $0.0001 per share, consisting of (a) 2,786,332 shares of Common Stock (the “2016 EIP Shares”) issuable pursuant to the Company’s 2016 Equity Incentive Plan, as amended (the “2016 EIP”), (b) 1,743,668 shares of Common Stock (the “2019 EIP Shares”) issuable pursuant to the Company’s 2019 Equity Incentive Plan (the “2019 EIP”) and (c) 180,000 shares of Common Stock (the “2019 ESPP Shares” and together with the 2016 EIP Shares and the 2019 EIP Shares, the “Shares”) issuable pursuant to Company’s 2019 Employee Stock Purchase Plan (the “2019 ESPP”, and together with the 2016 EIP, the 2019 EIP, the “Plans”).
In connection with this opinion, we have examined and relied upon (a) the Registration Statement and related prospectuses included therein, (b) the Company’s Amended and Restated Certificate of Incorporation and Amended and Restated Bylaws, each as currently in effect, (c) the Plans, and (d) the originals or copies certified to our satisfaction of such other records, documents, certificates, memoranda and other instruments as we deem necessary or appropriate to enable us to render the opinion expressed below. We have assumed 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. As to certain factual matters, we have relied upon a certificate of an officer of the Company and have not sought independently to verify 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 and issued in accordance with the Plans, respectively, and the Registration Statement and related prospectuses, will be validly issued, fully paid, and nonassessable (except as to shares issued pursuant to certain deferred payment arrangements, which will be fully paid and nonassessable when such deferred payments are made in full).
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