Originally Posted by
KARFA
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As noted, BA will not check through a bag on to a separate ticket even if both are BA flights. Therefore on arrival at T5 you will have to collect your bag and use the tube or HEX to get to T3 before checking it back in.
And due to the layout of T5, it's actually not too painful in this particular circumstance, since the direct access off the aircraft to landside will take you very swiftly down to the baggage carousel, and then it's easy access to HEX or the Tube. I would probably bias HEX since there's slightly less walking, but if the schedule display over the HEX ticket desk says 12 minutes or more you may as well take the tube. No tickets needed for HEX, you need a contactless payment card for the tube, but there's no cost. It would be about 5 to 10 minutes quicker via Flight Connections, but given your connection it scarcely matters, and there's no Immigration control involved here. Moreover you will have better control of where your bags are.