Originally Posted by
corporate-wage-slave
For the same reason - and for the benefit of anyone else searching here in the future - you cannot do this if entering T5 from landside, this only works if you are on a connection, and a non Domestic-Domestic one at that.
Presumably starting from T5 airside you can (if you
really want to) ride the shuttles to T5C, remain on them back to T5B (now in the arrivals flow), take the bus to T3, and then return to T5 as you describe (albeit that your ready to fly status will be strange, but probably corrected by somebody at T5 flight connections).
Myself I'd find this far too much effort, but then my target arrival time at T5 is typically 55 mins before departure.