Laboratory Corporation of America (LH) 8-K Labcorp Prices $400,000,000 IN2.300% Senior Notes Due 2024 and Cautionary Statement Regarding Forward-Looking Statements

Exhibit 5.1

Hogan Lovells US LLP 390 Madison Avenue New York, NY 10017 T   +1 212 918 3000 F   +1 212 918 3100 www.hoganlovells.com

November 18, 2019

Board of Directors

Laboratory Corporation of America Holdings

358 South Main Street

Burlington, NC 27215

Ladies and Gentlemen:

We are acting as counsel to Laboratory Corporation of America Holdings, a Delaware corporation (the “Company”), in connection with its registration statement onForm S-3, (FileNo. 333-234633) (the “Registration Statement”), filed with the Securities and Exchange Commission under the Securities Act of 1933, as amended (the “Act”) relating to the public offering of certain securities of the Company that may be offered and sold from time to time and on a delayed or a continuous basis as set forth in the prospectus dated November 12, 2019 (the “Prospectus”). This opinion letter is delivered in connection with the sale of $400,000,000 aggregate principal amount of the Company’s 2.300% Senior Notes due December 1, 2024 (the “2024 Notes”) and $650,000,000 aggregate principal amount of the Company’s 2.950% Senior Notes due December 1, 2029 (the “2029 Notes” and, together with the 2024 Notes, the “Notes”), pursuant to the terms of the Underwriting Agreement, dated November 18, 2019 (the “Agreement”), by and among the Company, BofA Securities, Inc., U.S. Bancorp Investments, Inc., and Wells Fargo Securities, LLC (for themselves and the other underwriters named therein), and as described in that supplement to the Prospectus dated November 18, 2019 filed with the Securities and Exchange Commission under Rule 424(b)(5) (the “Prospectus Supplement”).

The Notes will be issued pursuant to the Indenture dated November 19, 2010 (the “Indenture”), between the Company and U.S. Bank National Association (the “Trustee”), as supplemented by, in the case of the 2024 Notes, the Supplemental Indenture for the 2024 Notes, between the Company and the Trustee (together with the Indenture, the “2024 Notes Indenture”) and, in the case of the 2029 Notes, the Supplemental Indenture for the 2029 Notes, between the Company and the Trustee (together with the Indenture, the “2029 Notes Indenture”and, together with the 2024 Notes Indenture, the “Notes Indentures”). This opinion letter is furnished to you at your request to enable you to fulfill the requirements of Item 601(b)(5) of RegulationS-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

Hogan Lovells US LLP is a limited liability partnership registered in the District of Columbia. “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   Moscow   Munich   New York   Northern Virginia   Paris   Perth   Philadelphia   Rome   San Francisco   São Paulo   Shanghai   Silicon Valley   Singapore   Sydney   Tokyo   Warsaw   Washington, D.C.     Associated Offices:   Budapest   Jakarta   Riyadh   Shanghai FTZ   Ulaanbaatar   Zagreb.     Business Service Centers:   Johannesburg   Louisville.     Legal Services Center:   Berlin. For more information see www.hoganlovells.com

Laboratory Corporation of America Holdings - 2 - November 18, 2019

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). 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 New York law and the Delaware General Corporation Law, as amended. We express no opinion herein as to any other statutes, ordinances, rules, or regulations (and in particular we express no opinion as to any effect that such other statutes, rules or regulations may have on the opinions expressed herein).

Based upon, subject to and limited by the foregoing, we are of the opinion that following (i) due execution and delivery of each of the Notes Indentures, (ii) due authentication of the Notes by the Trustee, and (iii) due execution and delivery of the Notes by the Company in accordance with the terms of the Agreement, the Indenture and the applicable Notes Indenture, the Notes will constitute validly issued and binding obligations of the Company.

The opinion expressed above with respect to the valid and binding nature of obligations may be limited by bankruptcy, insolvency, reorganization, receivership, moratorium or other laws affecting creditors’ rights (including, without limitation, the effect of statutory and other law regarding fraudulent conveyances, fraudulent transfers and preferential transfers) and by the exercise of judicial discretion and the application of principles of equity, good faith, fair dealing, reasonableness, conscionability and materiality (regardless of whether the Notes are considered in a proceeding in equity or at law).

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 hereof.

We hereby consent to the filing of this opinion letter as Exhibit 5.1 to the Current Report on Form8-K of the Company to be filed with the Securities and Exchange Commission on the date hereof and thereby incorporated by reference as an exhibit to the Registration Statement and to the reference to this firm under the caption “Legal Matters” in the Prospectus and the Prospectus Supplement. In giving this consent, we do not thereby admit that we are an “expert” within the meaning of the Securities Act of 1933, as amended.

Very truly yours,

/s/ HOGAN LOVELLS US LLP

HOGAN LOVELLS US LLP