Capital Construction Fund Qualified Withdrawal Act of 2005 - Amends the Merchant Marine Act and the Internal Revenue Code to permit as qualified withdrawals from fishing capital construction funds any money used by retiring fishermen for the following purposes: (1) retiring an owner's commercial fishing vessels and related commercial fishing permits; (2) making a rollover contribution into an owner's individual retirement plan; (3) making a payment of an industry fee authorized by the fishing capacity reduction program; (4) acquiring a vessel monitoring system as a safety improvement for a fishing vessel; and (5) acquiring or constructing fishing gear designed to minimize or avoid bycatch.