Medicare Informed Choice Act of 2005 - Amends title XVIII (Medicare) of the Social Security Act to: (1) provide for an extended period of open enrollment during all of 2006 without late enrollment penalty; (2) give Medicare beneficiaries the opportunity to make a one-time change in prescription drug plan enrollment at any point in 2006; and (3) provide protection from loss of employment-based retiree health coverage upon enrollment for Medicare prescription drug benefit, including a Medicare Advantage-Prescription Drug benefit, during 2006.