If it's separate PNRs but also BA throughout then they will check your bags all the way through at IAD. Just have both PNRs handy on a post it note, and queue behind the most senior looking check-in agent.

The actual travel time from T5 to T1, gate to gate, can be below 40 minutes, so 2 hours 25 minutes is fine, Minimum Connection Time is 90 minutes. However if it does involve checked luggage and going landside personally I think it's a bit tight, especially if Uncle Murphy chucks your bag out last at T5. Go hand lugggage only?

Have a Plan B up your sleeve just in case the Washington flight is very late. BA won't guarantee your second flight but if you stay airside they will almost certainly look after you. If going landside you are reducing that cushion somewhat.