Recapture Excess Profits and Invest in Relief (REPAIR) Act of 2005 - Amends the Internal Revenue Code to: (1) impose on certain oil companies, for taxable years beginning in 2005 or 2006, an excise tax on 50 percent of their windfall profit from the sale of crude oil; (2) allow a tax deduction for the payment of such windfall profit tax; and (3) establish in the Treasury the Hurricane Relief Trust Fund to which windfall tax revenues will be paid to offset the cost of supplemental spending legislation enacted to aid Hurricane Katrina and Rita victims.