60 min is the minimum 'legal' connection time for T5 to T5, but you may like to consider that even if the first leg is slightly late (e.g. 15 min), you are likely to miss the 35 min conformance.

Even if you do get through the 35 min conformance, you may well have a hairy time in the security queue as I did earlier this month.

If you are on separate tickets, theoretically BA does not need to look after you for the connecting flight, although in reality most likely they will. Also if your connecting flight is the last flight of the day, you may well be rather inconvenienced.