Your going to hear a variety of things, but here is my take.
Impossible to predict, especially as it is a mess right now, but still difficult to say in normal times.
Your longest wait is usually immigration/passport check. They are supposed to be making it for US passport holders to use the e-gates, that should be quicker than the old line, but an hour is not unusual from deplaning to clearing immigration.
Baggage claim I have not done, you can search news reports and see the mess it has been in the last few weeks, should take less than a half hour, but right now, many just are not getting their bags. If you can do carry-on, that would be a wise move.
Customs is a non-issue, you have nothing to declare likely, just walk through the exit.
Figure another hour or so to get into London, so under normal conditions, 2 plus hours is typical planning, given current issues, 5 hours should be fine, more so without checked bags. I do not think I would be quick to prepurchase a rail ticket.