Historic Rehabilitation Enhancement Act of 2005 - Provides that: (1) the receipt of a state historic tax credit and the transfer, disposition, or refund of such credit shall not constitute income for income tax purposes, unless the taxpayer elects to include such tax credit amount in income; (2) the adjusted basis of property for which a state historic tax credit is allowed shall be reduced by the tax credit amount; and (3) the transfer or disposition of the state historic tax credit shall not affect or reduce qualified rehabilitation expenditures under the rehabilitation tax credit or trigger recapture of income.