Hurricane Disaster Mortgage Moratorium Act of 2005 - Establishes a moratorium, for the six-month period beginning on August 28, 2005, on any loan or other extension of credit that is secured by residential or commercial real estate that is located within an area in which the President has declared a major disaster area due to Hurricane Katrina or Rita. Prohibits: (1) any such loan from being found or declared delinquent or in default during such period; and (2) the moratorium period from being included within the length of time that a loan was otherwise in default.