I transferred from a DOH-ARN landing in T5 to BA ARN-LHR in T2 the day before yesterday.

Plenty of time so I collected my bags and walked as others have suggested. Taking the train seems to involve escalators down and lots of bother. It is about 10-20 minutes depending how fast you walk and I found it easy enough, just follow the signposts.

With 5 hours you'll have no problem at all, it will be very leisurely. On the way out, I was T5 to T5 and waited about an hour and a bit for check-in to open for the QR flight. That is quite boring.