Abandoned Mine Land Area Redevelopment Act of 2005 - Amends the Internal Revenue Code to allow a tax credit for investment in abandoned mine land area redevelopment bonds. Sets forth rules and formulae for the tax credit relating to the applicable credit rate, bond issuance and redemption, the amount of bonds designated, and a national volume cap. Specifies the purposes for such bonds, including: (1) the purchase, restoration, and redevelopment of abandoned mine land areas; (2) the cleanup of waterways on abandoned mine land areas from acid mine drainage and other pollution: (3) the provision of financial and technical assistance for infrastructure construction and upgrades on abandoned mine land areas; (4) research and development; and (5) other environmental and economic development relating to abandoned mine land areas.