I land Terminal 5 on Saturday 24th at 5am.
I fly out at Terminal 3 on Saturday 24th at 18.45.
May I go into London from Terminal 5 and come back into Terminal 3 after having a day in London?.
Are there any risks with the closure of transport at Terminal 5 on Saturday 24th.?
Saturday 24th
...of which month, Feb or Aug?
NOVEMBER 2023
I am assuming that you mean this Saturday, 25 November.
The only risk is that with the Elizabeth Line and Heathrow Express being closed for engineering, the tube is the only way to London by rail. So if the tube gets closed for some reason (technical, fire, whatever) there is no rail route available.
There would be work round solutions, but too convoluted to explain.
I would suggest taking the National Express coach in to London Victoria coach station. Multiple departures per hour, and coming back it drops you at Central Bus Station- linked to T3. It is as fast as the tube (sometimes faster on a good day). Just buy a ticket when you are clear of T5 on arrival, either on your 'phone or at the ticket machines.
this Saturday is the 25th, the 24th is Friday. Have you got your days right on both flights?
If you are taking an evening flight out of the US, you arrive in London the next day. So, if you leave on the 24th, you actually arrive in London on the 25th.