Safe Storage of Radiological Materials Act of 2005 - Directs the Secretary of Energy to submit to Congress: (1) an official notification of the final designation of an entity within the Department of Energy to have the responsibility of completing activities needed to provide a facility for safely disposing of all greater-than-Class C low-level radioactive waste; (2) a cost-estimate and a proposed schedule to complete an environmental impact statement and record of decision for a permanent disposal for greater-than-Class C radioactive waste; and (3) a plan to ensure the continued recovery and storage of greater-than-Class C low-level radioactive sealed sources that pose a security threat until a permanent disposal facility is available.