Fairness and Independence in Redistricting Act of 2005 - Prohibits a state that has been redistricted after an apportionment from being redistricted again until after the next apportionment of Representatives, unless the state is ordered by a court to conduct such a subsequent redistricting in order to: (1) comply with the U.S. Constitution; or (2) enforce the Voting Rights Act of 1965.
Requires such redistricting to be conducted through a plan developed by the independent redistricting commission established in the state, or if such plan is not enacted into law, the redistricting plan selected by the state's highest court or developed by a U.S. district court.
Sets forth provisions regarding: (1) establishment of a state independent redistricting commission; (2) development of a redistricting plan; (3) its submission to the state legislature; (4) selection of a plan, under specified conditions, by the state's highest court or the U.S. district court for the district in which the capital of the state is located; (5) special rules for redistricting conducted under a federal court order; and (6) Election Assistance Commission payments to states for carrying out redistricting.