Exhibit 5.1

October 17, 2014

Board of Directors

Cempra, Inc.

6320 Quadrangle Drive, Suite 360

Chapel Hill, NC 27517-8149

Ladies and Gentlemen:

We have acted as counsel to Cempra, Inc., a Delaware corporation (the “Company”), in connection with the sale of up to $25,322,647.90 of its common stock, par value $0.001 per share (the “Shares”), pursuant to a Registration Statement on Form S-3 (File No. 333-192754) (the “Registration Statement”) and the related Prospectus and Prospectus Supplement, as amended, filed with the Securities and Exchange Commission (the “Commission”). All of the Shares are to be sold by the Company as described in the Registration Statement and related Prospectus and Prospectus Supplement.

In connection with this opinion, we have examined the Registration Statement and related Prospectus and Prospectus Supplement, the Company’s Certificate of Incorporation and Bylaws, as currently in effect and such other documents, records, certificates, memoranda and other instruments as we deem necessary as a basis for this opinion. We have assumed the genuineness and authenticity of all documents submitted to us as originals, the conformity to originals of all documents submitted to us as copies thereof, and the due execution and delivery of all documents where due execution and delivery are a prerequisite to the effectiveness thereof. Further, we have assumed that the aggregate gross amount of Shares sold will not exceed $25,322,647.90.

Our opinion is expressed only with respect to the federal laws of the United States of America and the General Corporation Law of the State of Delaware. We express no opinion as to whether the laws of any particular jurisdiction other than those identified above are applicable to the subject matter hereof.

On the basis of the foregoing, and in reliance thereon, we are of the opinion that the Shares, when sold and issued in accordance with the Registration Statement and related Prospectus and Prospectus Supplement, will be validly issued, fully paid, and nonassessable.

We consent to the filing of this opinion as an exhibit to the Company’s Current Report on Form 8-K filed with the Commission on or about October 17, 2014.