We just returned from our Budapest-Prague vacation.
On the way over to Budapest we connected via terminal 5 at Heathrow and we had no problem with our baggage or connections.
On the way back from Prague, we again had to connect thru terminal 5 and again no baggage or connection problems.
We were very worried about the luggage problems that seem to plague terminal 5 but we had none.
Yes, they still are working on this terminal but that didn't seem to bother the connections.
Have a wonderful trip.
