QuickLinks -- Click here to rapidly navigate through this document

Exhibit 5.1

[COOLEY GODWARD LLP LETTERHEAD]

May 5, 2004

AMYLIN PHARMACEUTICALS, INC.
9360 Towne Centre Drive, Suite 110
San Diego, CA 92121

Ladies and Gentlemen:

You have requested our opinion with respect to certain matters in connection with the filing by AMYLIN PHARMACEUTICALS, INC., a Delaware corporation (the "Company"), of a Registration Statement on Form S-8 (the "Registration Statement") with the Securities and Exchange Commission, covering the offering of an aggregate of up to 750,000 shares of the Company's Common Stock, $.001 par value (the "Shares"), issuable pursuant to the Company's 2001 Employee Stock Purchase Plan (the "Plan").

In connection with this opinion, we have examined and relied upon the Registration Statement and related Prospectus, the Plan, the Company's Certificate of Incorporation and Bylaws, as amended, and the originals or copies certified to our satisfaction of such records, documents, certificates, memoranda and other instruments as in our judgment are necessary or appropriate to enable us to render the opinion expressed below. 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.

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

We consent to the filing of this opinion as an exhibit to the Registration Statement.

Very truly yours,

Cooley Godward LLP

/s/  THOMAS A. COLL Thomas A. Coll

QuickLinks

Exhibit 5.1