Exhibit 5

201 ST. CHARLES AVENUE NEW ORLEANS, LOUISIANA 70170-5100 504-582-8000 FAX 504-582-8583 www.joneswalker.com

September 10, 2018

CenturyLink, Inc.

100 CenturyLink Drive

Monroe, Louisiana 71203

Ladies and Gentlemen:

We have acted as special counsel to CenturyLink, Inc., a Louisiana corporation (the “Company”), in connection with the Company’s preparation of a registration statement on Form S-3 (the “Registration Statement”) to be filed with the Securities and Exchange Commission (the “Commission”). The Registration Statement relates to the registration of 500,000 shares of CenturyLink’s common stock, par value $1.00 per share the (“Common Stock”).

We have examined instruments, documents, and records which we deemed relevant and necessary for the basis of our opinion hereinafter expressed. In such examination, we have assumed the following: (a) the authenticity of original documents and the genuineness of all signatures; (b) the conformity to the originals of all documents submitted to us as copies; and (c) the truth, accuracy, and completeness of the information, representations, and warranties contained in the records, documents, instruments, and certificates we have reviewed.

Based upon the foregoing, we are of the opinion that the shares of Common Stock covered by this Registration Statement and to be issued by the Company after the filing of this Registration Statement are validly authorized shares of Common Stock and, when issued in the manner described in this Registration Statement, will be legally issued, fully paid, and non-assessable.

We hereby consent to the filing of this opinion as an exhibit to the Registration Statement and to the use of our name wherever it appears in the Registration Statement. In giving such consent, we do not consider that we are “experts” within the meaning of such term as used in the Securities Act of 1933, as amended, or the rules and regulations of the Securities and Exchange Commission issued thereunder, with respect to any part of the Registration Statement, including this opinion as an exhibit or otherwise.

Very truly yours,

/s/ Jones Walker LLP

Jones Walker LLP

JONES WALKER LLP

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