The gear speed indicator is (at least on my Scirocco) worked out on revs / speed. Doesn't actually take into account anything else. No electronic or physical gear position indicator so to speak. If you are precise with the revs you can hold it at the right speed and it will display you being in a gear when you are actually in neutral.
So that points to a possible electronics issue with a wheel speed sensor or a rev sensor. That being said there is a whole subroutine that goes on behind the actual displayed revs on the dial to even out variations. It only takes a few hundred rpm to be wrong.
Although it is very strange that it doesn't work for 5th gear. Is the gearbox on the car the stock gearbox? Has it had a longer ratio gearbox installed? On the Mk4 and Mk5 5 speed boxes it wasn't uncommon to fit a T4/T5 5th gear ring to reduce the effective final drive of that gear for better economy.
I hate to say it as it's really sh*te half of the time but have you scanned your car with VCDS to see if there are any faults.
You can also live log the cruise control.
As you say it's come into work I presume you are a mechanic so do I get a % of the repair cost if I figure it out?