<PAGE>
EXHIBIT 5.1
[LETTERHEAD FOR COOLEY GODWARD LLP]
November 21, 2000
Genomica Corporation
1745 38th Street
Boulder, Colorado 80301
Ladies and Gentlemen:
You have requested our opinion with respect to certain matters in connection
with the filing by Genomica Corporation, a Delaware corporation (the "Company"),
of a Registration Statement on Form S-8 (the "Registration Statement") with the
Securities and Exchange Commission (the "Commission") covering the offering of
up to 4,005,310 shares of the Registrant's Common Stock, par value $.001 per
share, pursuant to the Registrant's 2000 Equity Incentive Plan (the "Plan") (the
"Shares").
In connection with this opinion, we have (i) examined and relied upon the
Registration Statement and the related Prospectus, and (ii) reviewed the
Company's Certificate of Incorporation and Bylaws, and the originals or copies
certified to our satisfaction of such other records, documents, certificates,
memoranda and other instruments as in our judgment were necessary or appropriate
to enable us to render the opinion expressed below.
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
By: /s/ James C. T. Linfield
--------------------------
James C. T. Linfield
