Resource Efficient Appliance Incentives Act of 2005 - Amends the Internal Revenue Code to allow a business tax credit for the production of certain household appliances (clothes washers, dishwashers, and refrigerators) with a specified energy efficiency rating. Imposes an aggregate limitation of $75 million on such credit for all taxable years ($35 million for certain other appliances), and an annual limitation based on taxpayer gross receipts (two percent of taxpayer average annual gross receipts for the three previous taxable years).