Exhibit 5.1

Faegre Baker Daniels LLP

2200 Wells Fargo Center 90 South Seventh Street

Minneapolis Minnesota 55402-3901

Phone +1 612 766 7000

Fax +1 612 766 1600

April 20, 2015

CoLucid Pharmaceuticals, Inc.

15 New England Executive Park

Burlington, MA 01803

Ladies and Gentlemen:

We have acted as counsel to CoLucid Pharmaceuticals, Inc., a Delaware corporation (the “Company”), in connection with the Registration Statement on Form S-1 (File No. 333-203100) (the “Registration Statement”) filed by the Company with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Securities Act”), relating to the issuance by the Company of up to 6,164,000 shares of Common Stock, par value $0.001 per share (the “Common Stock”), of the Company in connection with the offering described in the Registration Statement (the “Shares”). The term “Shares” includes any additional shares of Common Stock registered by the Company pursuant to Rule 462(b) under the Securities Act in connection with the offering contemplated by the Registration Statement.

We have examined the Registration Statement and the form of amended and restated certificate of incorporation of the Company, which has been filed with the Commission as an exhibit to the Registration Statement. We also have examined the originals, or duplicates or certified or conformed copies, of such corporate and other records, agreements, documents and other instruments and have made such other investigations as we have deemed relevant and necessary in connection with the opinions hereinafter set forth. As to questions of fact material to this opinion, with your consent we have relied upon certificates or assurances of public officials and of officers and representatives of the Company

In rendering the opinions set forth below, we have assumed (i) the genuineness of all signatures, (ii) the legal capacity of natural persons, (iii) the authenticity of all documents submitted to us as originals, (iv) the conformity to original documents of all documents submitted to us as duplicates or certified or conformed copies, (v) the authenticity of the originals of such latter documents and (vi) that the Company will comply with all applicable notice requirements regarding uncertificated shares provided in the Delaware General Corporation Law.

Based upon the foregoing, and subject to the qualifications, assumptions and limitations stated herein, we are of the opinion that the Shares have been duly authorized by all necessary corporate action of the Company, and (a) when the Registration Statement becomes effective under the Securities Act, (b) when the pricing committee of the Company’s board of directors (the “Pricing Committee”) has taken all necessary action to approve the issuance and sale of the Shares, including determination of a specific number of Shares to be sold and a specific price for the sale of the Shares (which total number of shares shall not in total numbers exceed the total number of shares available under the Company’s amended and restated certificate of incorporation), (c) upon payment and delivery in accordance with the underwriting agreement in the form most recently filed with the Commission as an exhibit to the Registration Statement and approved by the Pricing Committee and (d) when the Shares shall have been duly registered on the books of the transfer agent and registrar therefor in the name or on behalf of the purchasers, will be validly issued, fully paid and nonassessable.

We do not express any opinion herein concerning any law other than the Delaware General Corporation Law (including the statutory provisions, all applicable provisions of the Delaware Constitution and reported judicial decisions interpreting the foregoing).

We hereby consent to the filing of this letter as Exhibit 5.1 to the Registration Statement and to the use of our name under the caption “Legal Matters” in the Prospectus included in the Registration Statement. We further consent to the incorporation by reference of this letter and consent into any registration statement filed pursuant to Rule 462(b) under the Securities Act with respect to the Shares. In giving this consent, we do not hereby admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the Commission.

This opinion is limited to the specific issues addressed herein, and no opinion may be inferred or implied beyond that expressly stated herein. This opinion speaks only as of the date the Registration Statement becomes effective under the Securities Act and we assume no obligation to revise or supplement this opinion thereafter.