Exhibit 5.1

Skadden, Arps, Slate, Meagher & Flom llp
One Manhattan West
New York, NY 10001
TEL: (212) 735-3000	FIRM/AFFILIATE OFFICES
FAX: (212) 735-2000	-----------
www.skadden.com	BOSTON
	CHICAGO
	HOUSTON
	LOS ANGELES
	PALO ALTO
	WASHINGTON, D.C.
	WILMINGTON
	-----------
	BEIJING
	BRUSSELS
	FRANKFURT
	HONG KONG
	LONDON
March 22, 2024	MUNICH
	PARIS
	SÃO PAULO
	SEOUL
	SHANGHAI
	SINGAPORE
	TOKYO
	TORONTO

Applied Therapeutics, Inc.
545 Fifth Avenue, Suite 1400
New York, New York 10017

Re:	Applied Therapeutics, Inc.
	Registration Statement on Form S-3

Ladies and Gentlemen:

We have acted as special United States counsel to Applied Therapeutics, Inc., a Delaware corporation (the “Company”), in connection with the registration for resale under the Securities Act of 1933 (the “Securities Act”), of an aggregate of 14,285,714 shares of the Company’s common stock, par value $0.0001 per share, consisting of (i) 12,285,714 shares (the “Existing Secondary Shares”) and (ii) 2,000,000 shares (the “Warrant Secondary Shares” and, together with the Existing Secondary Shares the “Secondary Shares”) issuable upon the exercise of 2,000,000 pre-funded warrants, with an exercise price of $0.001 per pre-funded warrant (the “Pre-Funded Warrants”), on behalf of the Selling Stockholders (as defined herein). We have been advised that the Existing Secondary Shares and the Pre-Funded Warrants were issued pursuant to a Securities Purchase Agreement (the “Securities Purchase Agreement”), dated February 27, 2024, by and among the Company and the selling stockholders named therein (the “Selling Stockholders”).

Applied Therapeutics, Inc. 

March 22, 2024 

Page 2

This opinion is being furnished in accordance with the requirements of Item 601(b)(5) of Regulation S-K under the Securities Act.

In rendering the opinions stated herein, we have examined and relied upon the following:

(a)            the registration statement on Form S-3 (the “Registration Statement”) to be filed on the date hereof by the Company relating to the Secondary Shares with the Securities and Exchange Commission (the “Commission”) under the Securities Act;

(b)            the prospectus, which forms a part of and is included in the Registration Statement;

(c)            an executed copy of the Securities Purchase Agreement;

Applied Therapeutics, Inc. 

March 22, 2024 

Page 3

(d)            an executed copy of a certificate of Shoshana Shendelman, Secretary of the Company, dated the date hereof (the “Secretary’s Certificate”);

(e)            a copy of the Company’s Amended and Restated Certificate of Incorporation as certified by the Secretary of State of the State of Delaware as of March 21, 2024, and certified pursuant to the Secretary’s Certificated (the “Amended and Restated Certificate of Incorporation”);

(f)            a copy of the Company’s Amended and Restated Certificate of Incorporation, as in effect as of the date the Existing Secondary Shares were issued, and certified pursuant to the Secretary’s Certificate (the “Prior Amended and Restated Certificate of Incorporation”);

(g)            a copy of the Company’s Amended and Restated Bylaws, as in effect as of the date hereof and certified pursuant to the Secretary’s Certificate (the “Amended and Restated Bylaws”);

(h)            a copy of the Company’s Amended and Restated Bylaws, as in effect as of the date the Existing Secondary Shares were issued, and certified pursuant to the Secretary’s Certificate (the “Prior Amended and Restated Bylaws”);

(i)             a copy of certain resolutions of the Board of Directors of the Company, adopted on February 26, 2024 and certain resolutions of the Pricing Committee thereof, adopted on February 27, 2024, each certified pursuant to the Secretary’s Certificate; and

Applied Therapeutics, Inc. 

March 22, 2024 

Page 4

(j)             executed copies of the Pre-Funded Warrants.

We have also examined originals or copies, certified or otherwise identified to our satisfaction, of such records of the Company and such agreements, certificates and receipts of public officials, certificates of officers or other representatives of the Company and others, and such other documents as we have deemed necessary or appropriate as a basis for the opinions stated below, including the facts and conclusions set forth in the Secretary’s Certificate.

In our examination, we have assumed the genuineness of all signatures, including electronic signatures, 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 photocopied copies, and the authenticity of the originals of such copies. With respect to our opinions set forth below, we have assumed that (i) the Company received in full the consideration for the Secondary Shares set forth in the Securities Purchase Agreement and the Pre-Funded Warrants, as applicable and the applicable resolutions of the Board of Directors of the Company approving the issuance of all such Secondary Shares, (ii) the issuance of the Existing Secondary Shares has been and the issuance of the Warrant Secondary Shares will be registered in the Company’s share registry, and (iii) the issuance of the Warrant Secondary Shares does not and the issuance of the Existing Secondary Shares did not violate or conflict with any agreement or instrument binding on the Company (except that we do not make this assumption with respect to (i) in the case of the Warrant Secondary Shares, the Amended and Restated Certificate of Incorporation and the Amended and Restated Bylaws, and (ii) in the case of the Existing Secondary Shares, the Prior Amended and Restated Certificate of Incorporation and the Prior Amended and Restated Bylaws, and in either case, those agreements or instruments expressed to be governed by the laws of the State of New York which are listed in the Company’s Annual Report on Form 10-K for the year ended December 31, 2023). 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 the Selling Stockholders and others and of public officials, including the facts and conclusions set forth in the Secretary’s Certificate and the factual representations and warranties set forth in the Securities Purchase Agreement.

We do not express any opinion with respect to the laws of any jurisdiction other than the General Corporation Law of the State of Delaware (the “DGCL”).

Applied Therapeutics, Inc. 

March 22, 2024 

Page 5

Based upon the foregoing and subject to the qualifications and assumptions stated herein, we are of the opinion that:

1.              the Warrant Secondary Shares being sold by the Selling Stockholders have been duly authorized by all requisite corporate action on the part of the Company under the DGCL and when issued in accordance with the terms of the Pre-Funded Warrants by the Company against payment of the exercise price therefor and registered in the Company’s share registry will be validly issued and fully paid and nonassessable; and

2.              the Existing Secondary Shares being sold by the Selling Stockholders have been duly authorized by all requisite corporate action on the part of the Company under the DGCL and are validly issued and fully paid and nonassessable.

Applied Therapeutics, Inc. 

March 22, 2024 

Page 6

We hereby consent to the reference to our firm under the heading “Legal Matters” in the prospectus forming part of the Registration Statement. We also hereby consent to the filing of this opinion with the Commission as an exhibit to the Registration Statement. In giving this consent, we do not thereby admit that we are within the category of persons whose consent is required under Section 7 of the Securities Act or the general Rules and Regulations under the Securities Act. This opinion is expressed as of the date hereof unless otherwise expressly stated, and we disclaim any undertaking to advise you of any subsequent changes in the facts stated or assumed herein or of any subsequent changes in applicable laws.

Very truly yours,

/s/ Skadden, Arps, Slate Meagher & Flom LLP

MJS