Exhibit 5.1

Hogan Lovells US LLP

Harbor East

100 International Drive

Suite 2000

Baltimore, MD 21202

T +1 410 659 2700

F +1 410 659 2701

www.hoganlovells.com

May 17, 2024

Board of Directors

Labcorp Holdings Inc.

358 South Main Street

Burlington, North Carolina 27215

To the addressee referred to above:

We are acting as counsel to Labcorp Holdings Inc., a Delaware corporation (the “Company”), in connection with its Registration Statement on Form S-8 (the “Registration Statement”), filed with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Act”) on May 17, 2024. The Registration Statement relates to the registration by the Company of up to: (i) 9,044,725 shares of common stock, par value $0.10 per share (“Common Stock”) under the Labcorp Holdings Inc. Amended and Restated 2016 Omnibus Incentive Plan (the “LTIP”) and (ii) 447,462 shares of Common Stock under the Labcorp Holdings Inc. Amended and Restated 2016 Employee Stock Purchase Plan (the “ESPP,” and together with the LTIP, the “Plans”). This opinion letter is furnished to you at your request to enable you to fulfill the requirements of Item 601(b)(5) of Regulation S-K, 17 C.F.R. § 229.601(b)(5), in connection with the Registration Statement.

For purposes of this opinion letter, we have examined copies of such agreements, instruments and documents as we have deemed an appropriate basis on which to render the opinions hereinafter expressed. In our examination of the aforesaid documents, we have assumed the genuineness of all signatures, the legal capacity of all natural persons, the accuracy and completeness of all documents submitted to us, the authenticity of all original documents, and the conformity to authentic original documents of all documents submitted to us as copies (including pdfs and conformed copies provided through the EDGAR System of the Commission). As to all matters of fact, we have relied on the representations and statements of fact made in the documents so reviewed, and we have not independently established the facts so relied on. This opinion letter is given, and all statements herein are made, in the context of the foregoing.

This opinion letter is based as to matters of law solely on the Delaware General Corporation Law, as amended. We express no opinion herein as to any other statutes, rules or regulations.

Based upon, subject to and limited by the foregoing, we are of the opinion that following (i) issuance of the Shares pursuant to the terms of the Plans, (ii) effectiveness of the Registration Statement and (iii) receipt by the Company of the consideration for the Shares specified in the applicable resolutions of the Board of Directors or a duly authorized committee thereof and in the Plans, the Shares will be validly issued, fully paid, and nonassessable.

Hogan Lovells US LLP is a limited liability partnership registered in the state of Delaware.  “Hogan Lovells” is an international legal practice that includes Hogan Lovells US LLP and Hogan Lovells International LLP, with offices in:  Alicante  Amsterdam  Baltimore  Beijing  Birmingham  Boston  Brussels  Colorado Springs  Denver  Dubai  Dusseldorf  Frankfurt  Hamburg  Hanoi  Ho Chi Minh City  Hong Kong  Houston  Johannesburg  London  Los Angeles  Luxembourg  Madrid  Mexico City  Miami  Milan  Minneapolis  Monterrey  Munich  New York  Northern Virginia  Paris  Philadelphia  Rome  San Francisco  São Paulo  Shanghai  Silicon Valley  Singapore  Sydney  Tokyo  Warsaw  Washington, D.C.   Associated Offices:  Budapest  Jakarta  Riyadh  Shanghai FTZ  Ulaanbaatar.   Business Service Centers:  Johannesburg  Louisville.   Legal Services Center:  Berlin.  For more information see www.hoganlovells.com

Labcorp Holdings Inc. - 2 - May 17, 2024

This opinion letter has been prepared for use in connection with the Registration Statement. We assume no obligation to advise of any changes in the foregoing subsequent to the effective date of the Registration Statement.

We hereby consent to the filing of this opinion letter as Exhibit 5.1 to the Registration Statement. In giving this consent, we do not thereby admit that we are an “expert” within the meaning of the Act.

Very truly yours,

/s/ HOGAN LOVELLS US LLP

HOGAN LOVELLS US LLP