Family Telephone Connection Protection Act of 2005 - Amends the Communications Act of 1934 to direct the Federal Communications Commission (FCC) to consider the following types of regulation of inmate telephone service: (1) prescribing a maximum uniform per-minute rate (paid to telephone service providers); (2) prescribing a maximum uniform service connection or other per-call rate; (3) prescribing variable maximum rates depending on factors such as carrier costs or the size of the correctional facility; (4) requiring providers of inmate telephone service to offer both collect calling and debit account services; (5) prohibiting the payment of commissions by such providers to administrators of correctional facilities; and (6) requiring such administrators to allow more than one service provider at a facility so that prisoners have a choice.