Exhibit 5.1

[LETTERHEAD OF SKADDEN, ARPS, SLATE, MEAGHER & FLOM LLP]

March 23, 2023

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

Re: Applied Therapeutics, Inc.
Registration Statement on Form S-8

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 Statement on Form S-8 of the Company (together with the exhibits thereto, the “Registration Statement”) to be filed on the date hereof with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933 (the “Securities Act”), relating to the registration of 3,713,943 shares (the “Shares”) of the Company’s common stock, $0.0001 par value per share, available for future issuance under the Company’s 2019 Equity Incentive Plan (the “Plan”).

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 opinion stated herein, we have examined and relied upon the following:

(a)            the Registration Statement in the form to be filed with the Commission on the date hereof;

(b)            the Plan;

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

Applied Therapeutics, Inc.

March 23, 2023

Page 2

(d)            a copy of the Company’s Amended and Restated Certificate of Incorporation (the “Amended and Restated Certificate of Incorporation”), certified by the Secretary of State of the State of Delaware as of March 23, 2023, and certified pursuant to the Secretary’s Certificate;

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

(f)            copies of certain resolutions of the Board of Directors of the Company, adopted on April 24, 2019 and March 21, 2023, and certified pursuant to the Secretary’s Certificate.

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 opinion 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. In making our examination of executed documents, we have assumed that the parties thereto, other than the Company, had the power, corporate or other, to enter into and perform all obligations thereunder and have also assumed the due authorization by all requisite action, corporate or other, and the execution and delivery by such parties of such documents and the validity and binding effect thereof on such parties. As to any facts relevant to the opinion 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 others and of public officials, including the facts and conclusions set forth in the Secretary’s Certificate.

In rendering the opinion stated herein, we have also assumed that (i) an appropriate account statement evidencing the Shares credited to a recipient’s account maintained with the Company’s transfer agent has been or will be issued by the Company’s transfer agent, (ii) the issuance of the Shares will be properly recorded in the books and records of the Company, (iii) each award agreement pursuant to which rights to acquire Shares or other awards are granted pursuant to the Plan will be consistent with the Plan and will be duly authorized, executed and delivered by the parties thereto, (iv) the consideration received by the Company for each of the Shares delivered pursuant to the Plan shall not be less than the per share par value of the Shares and (v) the issuance of the Shares does not violate or conflict with any agreement or instrument binding on the Company (except that we do not make this assumption with respect to the Amended and Restated Certificate of Incorporation or the Amended and Restated Bylaws.

Applied Therapeutics, Inc.

March 23, 2023

Page 3

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”).

Based upon the foregoing and subject to the qualifications and assumptions stated herein, we are of the opinion that the Shares have been duly authorized by all requisite corporate action on the part of the Company under the DGCL and, when the Shares are issued to the participants in accordance with the terms and conditions of the Plan and the applicable award agreement for consideration in an amount at least equal to the par value of such Shares, the Shares will be validly issued, fully paid and nonassessable.

We 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 included in 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.

Very truly yours,

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

MJS