Torture Victims Relief Reauthorization Act of 2005 - Amends the Torture Victims Relief Act of 1998 to authorize appropriations for FY2006-FY2007 to: (1) the Department of Health and Human Services (HHS) to provide grants to programs in the United States to cover the costs of services provided by domestic treatment centers in the rehabilitation of victims of torture (including treatment of the physical and psychological effects of torture), social and legal services, and research and training of health care providers outside of treatment centers or programs to enable them to provide such services; (2) the President for grants to treatment centers and programs in foreign countries that carry out projects and activities specifically designed to treat victims of torture for the physical and psychological effects of torture; and (3) the United Nations Voluntary Fund for Victims of Torture.