Privacy Officer With Enhanced Rights Act of 2005 or POWER Act - Amends the Homeland Security Act of 2002 with respect to the authorities of the privacy officer of the Department of Homeland Security. Specifies the privacy officer's investigative authority to: (1) have access to all records and other materials available to the Department relating to programs and operations for which the privacy officer has responsibilities; (2) make necessary or desirable investigations and reports on the administration of Department programs and operations; (3) require by subpoena the production, by persons other than Federal agencies, of all information and other data and documentary evidence necessary to performance of the privacy officer's functions; (4) administer oaths, affirmations, or take affidavits; and (5) take any other action that may be taken by the Inspector General of the Department, as necessary to require Department employees to produce documents and answer questions relevant to performance of the privacy officer' s functions.