Originally Posted by AlicorporateUK
Moreover, presuming that you'll be travelling with a luggage, you'll not have to collect it in FCO if flying with AZ or DL and that can save you quite a bit of time, also considering that luggage delivery in Rome can often prove to be rather tricky.
That said, you will have to clear customs and change Terminal (from T5 to T1) in any case.
Good luck and have great time in Italy.
T5 is only a check-in terminal for 'dangerous' carriers AA, DL, CO, UA, US & EL AL (after check-in and Immigration/Security you take a bus to T3 - boarding is at T3) - arrivals are at non-Schengen T3.
Also.. Italy is different from the US - you clear Customs at the final domestic destination - as long as AA would check your baggage through to BDS (they would be oblidged to do this if you are travelling on the same ticket; it is up to them - and oneWorld carriers are normally reluctant to do this - if you travel on 2 separate tickets) - you will only pick your baggage in BDS. So - as long as the baggage is checked through - you only need to clear Immigration (at T3) and run to T1 for a domestic boarding. T1/2/3 are interconnected, so no need to get outside of the building - just follow the signs.
Now.. 1:25 is a tight connection... also if you travel on 2 separate tickets, and do not make the connection please be aware that Europe has not adopted a US 'stand-by culture' - they will not put you on a next flight - you will have to purchase a new ticket (or at least pay a penalty plus an upgrade - actually a new ticket might be cheaper).