State and Local Housing Flexibility Act of 2005

State and Local Housing Flexibility Act of 2005 - Flexible Voucher Act of 2005 - Authorizes the Secretary of Housing and Urban Development (HUD) to make grants to public housing agencies to provide tenant-based and project-based rental assistance, and tenant-based first-time homeownership assistance to low-income individuals. (This program replaces the housing choice voucher program.) Sets forth program provisions.

Continues the following section 8 (United States Housing Act of 1937) programs for current beneficiaries: (1) tenant-based rental or homeownership assistance; (2) project-based voucher assistance; and (3) elderly and disabled family assistance.

Public Housing Rent Flexibility and Simplification Act of 2005 - Amends the United States Housing Act of 1937 to revise public housing rental payment provisions to provide that public housing dwelling units shall be rented only to and occupied by low-income families that do not own a significant interest in real property and do not have assets exceeding an amount established by the Secretary at the time of their initial occupancy.

Requires income reviews at least once every two years, except for elderly or disabled families who shall be reviewed at least once every three years.

Sets forth rent structure guidelines.

Authorizes a public housing agency: (1) to allow a police officer who is not otherwise eligible for public housing residence to reside in a public housing dwelling unit in order to increase security for residents; (2) that owns or operates fewer than 250 public housing dwelling units to lease on a month-to-month basis to over-income families if no eligible families apply for housing assistance for that month; and (3) to establish tenant escrow savings accounts.

Moving to Work Program Act of 2005 - Amends the Housing Act of 1937 to direct the Secretary to establish the Moving to Work Program, under which eligible public housing agencies may combine operating assistance, modernization assistance, and assistance provided under this Act to provide housing assistance for low-income families and services to facilitate the transition to work. Sets forth program provisions.