To amend the Fair Labor Standards Act of 1938 to provide for an increase in the Federal minimum wage.

Fair Minimum Wage Act of 2005 - Amends the Fair Labor Standards Act of 1938 to increase the federal minimum wage to: (1) $5.85 an hour, beginning on the 60th day after enactment of this Act; (2) $6.55 an hour, beginning 12 months after that 60th day; and (3) $7.25 an hour, beginning 24 months after that 60th day. Makes federal minimum wage requirements applicable to the Commonwealth of the Northern Mariana Islands. Sets forth a transition period during which a specified minimum wage there shall be gradually increased to equal the federal minimum wage.