Hydraulic Fracturing Safety Act of 2005 - Amends the Safe Drinking Water Act to: (1) include hydraulic fracturing within the definition of underground injection for purposes of such Act; (2) define hydraulic fracturing as the process of creating a fracture in a reservoir rock, through the injection of fluids and propping agents, for the purpose of reservoir stimulation during oil and gas production activities; (3) prohibit, during the hydraulic fracturing process, the use of diesel fuel or any other material that the Administrator of the Environmental Protection Agency (EPA) has listed as a priority pollutant under the Federal Water Pollution Control Act; and (4) require the Administrator to regulate hydraulic fracturing and ensure that state programs under the Safe Drinking Water Act regulate hydraulic fracturing in accordance with this Act.