My mum and dad (GFL - if that possibly makes a difference) had a T3-T5 connection (QA->BA, separate tickets, including checked luggage) and had a similar experience. They went through the First Wing after collecting their luggage off their DXB flight and after a phone call from the check-in agent were allowed to proceed (but told to get a move on!). Checked bags made it to EDI too.

I find conformance a stange thing, as I've had flights where I've been so panicked getting to T5 then after passing through security I have time for a drink and some food in the lounge.