What Frank said is correct. T5 (a former hangar/warehouse) is only a check-in/security processing area for US based and Israeli based airlines. Once the check in and security procedures are completed, passengers are shuttled (on the sterile airside area) back to T3 by bus. T3 is where the airplanes actually dock.
The separation of US based airlines (and El Al) was created following the deadly terrorist attack of December 1985 (which was simultaneous with the attack at Vienna airport), when Palestinian terrorists targeted passengers in line at the check in of TWA, Pan-Am and El Al with assault rifles and grenades. Following that attack, initially those airlines' check in areas were placed in a separate, heavily guarded area within T3, then several years ago, they decided to move them to this newly created T5 area altogether.
The arrival of passengers is still at T3 for all airlines. The fire has not changed that. The only change caused by the fire is that now some Asian airlines' check-in is temporarily moved to T5 as well.
http://www.adr.it/en/web/aeroporti-di-roma-en-/pax-fco-airport-map