Hurricane Katrina Tax Relief Act of 2005 - Amends the Internal Revenue Code to provide tax relief to Hurricane Katrina victims, including by: (1) permitting penalty-free withdrawals from tax-exempt retirement accounts for disaster relief; (2) allowing certain tax credits for employers and employees affected by Hurricane Katrina; (3) increasing, between August 28 and December 31, 2005, the limitation on individual and corporate charitable cash contributions; (4) permitting tax-free distributions from individual retirement accounts for charitable purposes relating to Hurricane Katrina disaster relief; (5) allowing individuals (in addition to corporations) to claim a tax deduction for charitable contributions of food inventories; (6) allowing an additional personal tax exemption for the housing of individuals displaced by Hurricane Katrina; (7) increasing the standard mileage rate for the tax deduction for charitable usage of a passenger automobiles; (8) excluding from gross income cancellation of certain indebtedness owned by Hurricane Katrina victims; (9) suspending limitations on casualty losses incurred by Hurricane Katrina victims; and (10) authorizing the Secretary of the Treasury to disclose to state officials information concerning the tax status of certain charitable organizations.