<Page>

                                                                       Exhibit 5

                                December 19, 2003

Transgenomic, Inc.
12325 Emmet Street
Omaha, NE  68164

     Re:       Transgenomic, Inc. Common Stock

Ladies and Gentlemen:

     We have acted as counsel for Transgenomic, Inc., a Delaware corporation
(the "Company"), in connection with the filing of a Registration Statement on
Form S-3 (the "Registration Statement") under the Securities Act of 1933, as
amended (the "Act"), with respect to the registration of 1,505,909 shares of
common stock of the Company (the "Shares") which may be issued to Laurus Master
Fund, Ltd. ("Laurus") upon conversion of a $2.0 million Secured Convertible
Minimum Borrowing Note from the Company to Laurus (the "Note") and upon the
exercise of Warrants issued to Laurus and TN Capital Equities, Ltd. in
connection therewith (the "Warrants"). This opinion is being furnished in
accordance with the requirements of Item 16 of Form S-3 and Item 601(b)(5)(i) of
Regulation S-K.

     In the course of such representation, we have examined, among other things,
the terms of the Note, the Warrants and other documents associated therewith and
such corporate records, certificates of public officials and other documents we
deemed relevant and appropriate. Based on the foregoing, we are of the opinion
that the Shares when issued pursuant to the terms of the Note and the Warrants
will be legally issued, fully paid and nonassessable.

     We hereby consent to the filing of this opinion letter as an exhibit to the
Registration Statement and to the reference to this firm under the heading
"Legal Opinions" in the prospectus which is part of the Registration Statement.
In giving this consent, we do not thereby admit that we are within the category
of persons whose consent is required under Section 7 of the Act, the rules and
regulations of the Securities and Exchange Commission promulgated thereunder, or
Item 509 of Regulation S-K.

     This opinion letter is rendered as of the date first written above. We
disclaim any obligation to advise you of facts, circumstances, events or
developments which may be brought to our attention after the effective date of
the Registration Statement and which may alter, affect or modify the opinion
expressed herein. This opinion letter supercedes any opinion letter previously
delivered by us with respect to the registration of the Shares. Our opinion is
expressly limited to the matters set forth above and we render no opinion,
whether by implication or otherwise, as to any other matters relating to the
Company or the Shares.

                                Very truly yours,


                               /s/ Kutak Rock LLP