Exhibit 5

April 19, 2004

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 2,557,842 shares of common stock of the Company (the ”Shares”) which may be issued to Laurus Master Fund, Ltd. (“Laurus”) and TN Capital Equities, Ltd. (“TN Capital”) upon conversion of a $3.0 million Secured Convertible Minimum Borrowing Note from the Company to Laurus (the “Revolving Note”), upon the conversion of a $2.75 million Convertible Term Note from the Company to Laurus (the “Term Note”) and upon the exercise of Warrants issued to Laurus and TN Capital 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 Revolving Note, the Term 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 Revolving Note, the Term 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. 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,

Kutak Rock LLP

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