My family and I are flying out of London around the same time to different destinations from different terminals. I want to help my wife check-in and go through security and immigration in terminal 5, and then head to my flight out of terminal 3. Can I do my checkin and security at terminal 5? Or is that not allowed?
So, first things first. Terminal 5 is very far from the other terminals at Heathrow, and it would take a lot of time to get from T5 to T3. The other thing to note is that there is no way, as far as I know, to get to T3 airside. You would have to go through security screening at both terminals; all in all, I would not recommend trying to accompany your wife unless you have at least an hour to spare. If there is a particular reason that she needs assistance (e.g. her English isn't particularly good), the airport or airline staff may be able to help.
Now, as for whether or not you're allowed to enter T5 airside in the first place. You will not be able to enter with a boarding pass issued for a flight leaving from T3. However, you can ask the BA staff at T5 to issue you with a gate pass; essentially, it's a pass that will let you go through security at T5. I'm afraid I don't know their policy on gate passes, but you might call them and ask them about it.
As for check-in, you would have to do that either online or at T3. It would not be possible to check in at T5 as your airline would not have a check-in counter there.