Katrina Assistance Tax Relief Incentives for Necessities Act of 2005 or the KATRINA Act of 2005 - Amends the Internal Revenue Code to: (1) designate Hurricane Katrina disaster victims as members of a targeted group for purposes of the work opportunity tax credit; (2) allow a tax credit, up to $1,000 annually, for individuals who house Hurricane Katrina disaster victims free of charge; (3) allow a tax credit, up to $5,000, for Hurricane Katrina disaster victims who purchase a principal residence in the Hurricane Katrina disaster area; and (4) increase the per capita housing credit ceiling for the low-income housing tax credit for Alabama, Louisiana, and Mississippi for 2006 and 2007 (from $1.75 to $3.70 multiplied by the state's population) and to waive certain requirements for such credit.