I think the issue here is that BA558 is the last BA flight to FCO of the day so I guess that the OP would have to be put up for the night and go on a flight the day after.

However, 1 hour is enough to make a connect at T5, even if you arrive at T5C and have to get to B or A. I did a T5C to T5A once in 40 minutes and had about 10 minutes to spare.

Remember to check the boards when you come off the plane as FCO may be at a B or C gate. For T5C->T5C or T5B->T5B You can connect within each building without going all the way to T5A and coming back.

If you land at T5C and departing at T5B go down to the train and get off at the first stop for T5B where you can go through connections in T5B.

Having said all that, I think flights back from the US are generally quick at the moment so you may well make up time on the way.