On arrival you can exit landside instead of taking the connections route. Just go through immigration as if an arriving passenger.

If you have already gone through connections and security and are already in the airside departures area you have two routes out:

1. You can speak to a BA member of staff, there is an escorted route which takes place on the hour every hour (from near gate A10 I think), and if you miss it you will have to wait up to an hour for the next one.
2. You can take the TTS to T5C, stay on the transit, and then when you come back to T5A you will be in the arrivals stream and arrive at the FCC. You will have to cross the UK border to go landside just like any arriving passenger, so you will need a passport to use this option.

Bear in mind if you use option 2, and want to go back airside later on using the same boarding pass you will have to get a BA member of staff to first un-register you as ‘Ready to Fly’. When you original went to go airside at T5 using your boarding pass you would have been marked as ‘Ready to Fly’ and you need to be unregistered so you can re-enter T5 airside - without unregistering your boarding pass will not work when you try your boarding pass at the landside gates just before security.