Exhibit 5

September 12, 2003

Nucor Corporation

2100 Rexford Road

Charlotte, North Carolina 28211

Re: Registration Statement on Form S-8

Dear Madam and Sirs:

We are acting as counsel for Nucor Corporation, a Delaware corporation (the “Company”), in connection with the registration on a Registration Statement on Form S-8 (the “Registration Statement”) under the Securities Act of 1933, as amended, of the offer and sale of up to 5,000,000 shares of common stock, par value $0.40 per share, of the Company (the “Shares”) to be issued upon the exercise of options under the Company’s 2003 Key Employees Incentive Stock Option Plan (the “Plan”).

In rendering our opinion, we have examined, and are familiar with, and have relied as to factual matters solely upon, originals or copies certified, or otherwise identified to our satisfaction, of such documents, corporate records or other instruments as we have deemed necessary or appropriate for the purpose of the opinion set forth herein, including, without limitation (i) the Plan, (ii) the Company’s certificate of incorporation and bylaws, as amended to date, (iii) all actions of the Company’s board of directors recorded in the Company’s minute book and (iv) a specimen of the form of certificate evidencing the Shares.

Based upon and subject to the foregoing, we are of the opinion that the Shares are duly authorized and, when issued and delivered pursuant to the terms of the Plan and the terms of any agreement relating to any of the options granted thereunder, will be validly issued, fully paid and nonassessable.

We hereby consent to the filing of this opinion letter as Exhibit 5 to the Registration Statement.

Very truly yours,

MOORE & VAN ALLEN PLLC

/s/    MOORE & VAN ALLEN PLLC