After some more testing, I’m now pretty confident that the problem lies with the Beocom 5.
I was digging around my spare room and found that I had another Beoline Mk2, so I exchanged it, and I had the same problem. The Beocom 5 won’t find it, and the Beocom 6000 will link to it, but continues to say ‘Not Base 1’ if I try to go into the base service menu.
I also found I had a Beocom 6000 pyramid PSTN, so I tried to connect the Beocom 5 to that too. Same result – it continues to search for the base, but it doesn’t find it (and yes, the base is in discoverable mode).