Exhibit 5.1

ALSTON&BIRD LLP

90 Park Avenue

New York, NY 10016

212-210-9400

Fax:212-210-9444

www.alston.com

February 5, 2016

Global Payments Inc.

10 Glenlake Parkway

North Tower

Atlanta, Georgia 30328

Ladies and Gentlemen:

We are acting as counsel to Global Payments, Inc., a Georgia corporation (the “Company”) in connection with the registration statement on Form S-4 filed by the Company with the Securities and Exchange Commission (the “Commission”) pursuant to the Securities Act of 1933, as amended (the “Securities Act”), on February 5, 2016 (the “Registration Statement”) for the registration of shares (the “Shares”) of common stock, without par value, of the Company (the “Common Stock”). The Company will issue the Shares to stockholders of Heartland Payment Systems, Inc. (“Heartland”) pursuant to the terms and conditions of an Agreement and Plan of Merger dated December 15, 2015 (the “Merger Agreement”) by and among the Company, Heartland, and various merger subs. This opinion is furnished to you at your request in accordance with the requirements of Item 21 of the Commission’s Form S-4 and Item 601(b)(5) of Regulation S-K promulgated under the Securities Act.

We have examined the Second Amended and Restated Articles of Incorporation of the Company, the Sixth Amended and Restated Bylaws of the Company, records of proceedings of the Board of Directors, or committees thereof, deemed by us to be relevant to this opinion letter, and the Registration Statement. We also have made such further legal and factual examinations and investigations as we deemed necessary for purposes of expressing the opinion set forth herein. In rendering such opinion, we have relied as to factual matters upon the representations, warranties and other statements made in the Merger Agreement.

As to certain factual matters relevant to this opinion letter, we have relied conclusively upon originals or copies, certified or otherwise identified to our satisfaction, of such records, agreements, documents and instruments, including certificates or other comparable documents of officers of the Company and of public officials, as we have deemed appropriate as a basis for the opinion hereinafter set forth. Except to the extent expressly set forth herein, we have made no independent investigations with regard to matters of fact, and, accordingly, we do not express any opinion as to matters that might have been disclosed by independent verification.

Atlanta • Charlotte • Dallas • Los Angeles • New York • Research Triangle • Silicon Valley • Ventura County • Washington, D.C.

Based upon the foregoing and subject to the limitations, qualifications, exceptions and assumptions set forth herein, we are of the opinion that the Shares have been duly authorized by all necessary corporate action of the Company and when issued pursuant to the terms and conditions of the Merger Agreement, will be validly issued, fully paid and nonassessable.

Our opinion set forth herein is limited to the laws of the State of Georgia and the federal law of the United States, and we do not express any opinion herein concerning any other laws.

This opinion letter is provided to the Company for its use solely in connection with the transactions contemplated by the Merger Agreement and may not be used, circulated, quoted or otherwise relied upon for any other purpose without our express written consent. The only opinion rendered by us consists of that set forth in the fourth paragraph of this letter, and no opinion may be implied or inferred beyond the opinion expressly stated. Our opinion expressed herein is as of the date hereof, and we undertake no obligation to advise you of any changes in applicable law or any other matters that may come to our attention after the date hereof that may affect our opinion expressed herein.

We consent to the filing of this opinion letter as an exhibit to the Registration Statement and to the use of our name under the heading “Legal Matters” in the Registration Statement. In giving such 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 rules and regulations of the Commission thereunder.

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