MCT (minimum connection time) at LHR T5 is 60 minutes. I just declined such a connection as if your incoming flight is more that a few minutes late, you will not make it. You need to pass the conformance check, where your papers are checked, but before security, 35 minutes before scheduled departure of the connecting flight. T5 is fairly well signposted, your mother has to blindly keep following signs for "Flight Connections". Depending on where her incoming plane ends up, this could be short and simple, from T5B would require a short train trip, or if the plane is on a remote stand, the pleasure of a bus ride.
There will be no need to go through immigration as you are doing an international to international connection.
If the two segments have been issued on a single ticket and the incoming flight is delayed, BA will indeed rebook on to the next flight and is supposed to provide hotel accommodation. The problem could be that in that case, you would have to go through immigration to go landside at LHR.