LHR connection quickest route

Evening,
Due to fly vs07 LHR - LAX in a couple of weeks, and taking advantage of the AMS trick. Wanting to make the most of my time in the clubhouse wouldn't mind some advice on quickest connection route. I land at T5 with BA 07.30 and due to fly at 11.15. I would consider running but have stress fracture. Just reading through previous threads just undecided if flight connections is the fastest way, and willing to miss private security channel.

Thank you

Evening,
Due to fly vs07 LHR - LAX in a couple of weeks, and taking advantage of the AMS trick. Wanting to make the most of my time in the clubhouse wouldn't mind some advice on quickest connection route. I land at T5 with BA 07.30 and due to fly at 11.15. I would consider running but have stress fracture. Just reading through previous threads just undecided if flight connections is the fastest way, and willing to miss private security channel.

Thank you

I would use flight connections this way you don't need to clear passport controll and customs.