Hi Nick,
The 'usual' reason for the car to stick in 5th gear is an issue inside the selector box on the gearbox - but it can be caused by cable adjustment (unlikely) or gearbox fault (also unlikely).
It happened on mine, and I had to do a couple of 'roadside' repairs with minimal tools - so it isn't difficult.
Basically, you need to undo the 4 (IIRC) bolts from the selector box to the gearbox - and lift the selector box out of the way. You then need to use a screwdriver (or similar) to replicate the bit of the selector box which engages with the gearbox. You should be able to easily select whichever gear you require by hand. Assuming that you can, then you have ruled out a problem with the gearbox, and can then drive the car in whatever gear you have 'chosen' - 3rd will get you most places, if push comes to shove..... but this is only a necesity if it is the cables at fault.
Okay, so you have got the gearbox into 4th (or whatever you choose), then you need to get the gearstick into the right place for 4th (and the selectors inside the box).
This is where I would expect you to instantly see the problem...... the shaft which runs through the box between the 5th Gear and reverse positions has a metal cam and spring between the 2 positions. If the pin which holds this cam onto the shaft becomes undone or broken, the cam will slip and jam the mechanism (it is this cam which you overcome with the lever when you select reverse from the drivers seat). The whole point of it is so that you can't engage reverse whilst driving, but if it slips, it will allow you to select 5th, but not de-select it (hence the original problem).
Once you manipulate the contents of the selector box to match the gearbox, simply bolt it back together again. In this state it will allow you to select and drive in 1st, 2nd, 3rd, 4th and reverse without any issues..... but if you 'forget' and go into 5th it will stay there! This would get you to a garage, but to be honest, if you get to this point you may as well just fix it yourself.
You have 2 choices (or 3 if you have a 'spare' selector box) - either work out visually where the cam should locate (pull against the spring and it should be obvious) and refit it with a new pin/bolt/screw/whatever..... or if you're in a wet layby at the side of the road in rural Herefordshire on a rainy night...... remove the cam from the shaft and chuck it in the toolbox along with the spring intending to replace it at a suitable time.
Option 1 will be sorted.
Option 2 will do for at least 6 years as long as you remember not to try and engage reverse from 5th whilst driving at 70mph because you have 6 gears in your other car!!!
The whole job can take less than 15 minutes - no gasket is necessary between the selector box and the gearbox (as it isn't below the oil level), but you can use a smear of blue instant-gasket-in-a-tube if you want to, Silicone sealant, or similar. You only need a 13mm socket,spanner or very strong fingers - screwdriver and long-nose pliers.
Edit - Written whilst RIP was posting, but at least i know the full answer