Social Security Fairness Act of 2005 - Amends title II (Old Age, Survivors and Disability Insurance) (OASDI) of the Social Security Act to: (1) provide that, if an OASDI recipient dies during the first 15 days of a month, the last payment of the monthly benefit for that month shall be half the usual benefit amount; and (2) provide for an increase in lump-sum death payments.