5th gear whining noise.
 

When I'm in 5th gear, applying gas, there is a high pitched whining noise coming from the engine area. It is only when I am in 5th gear, and only when I am on the gas. Increasing the speed increases the pitch. If I'm off the gas, or with the clutch in, there's no noise, and all other gears are fine.
If 5th gear goes bust, will I still be able to drive in the other 4 gears?

Yep mine was like that, slight whine in 5th. Then i got a grumble in any gear on load, now it does it off and on load........final drive pinion me thinks due to go pop!

Have you checked your gearbox oil? When I had this problem on a Renault, it turned out to be low gearbox oil.

I bought a funnel and a plastic hose yesterday. Planning to change the oil, but first I'd like to check the level. There's no dipstick so I'll have to stick a drinking straw or something into the refilling hole to see if the level is low or not.
Apart from a low level, old oil can't be good. No mention of an oil change in the service book which means that the oil is 17 years old and overdue for a change.

Not sure if I found the correct draining plug. I found one that fits a 16 mm socket and one larger with a square hole in the middle. Loosened the 16 mm one and a few drops of oil came out.
I refilled it. It took 3.2 litres. Capacity is 3.4 litres.
Where has the oil gone? -And for how long has it been running with a dry gearbox?
I'll have to check for leaks.
To early to tell whether the wining is gone or not. Have to take a long drive in 5th gear.

Drive shaft oil seals a possible oil loss point, has the gearbox been out?

No. the box has never been out.
There was some oil spillage underneath the gearbox, but I've never noticed any leaks on the ground.
Lots of snow here in winter, so I would have noticed oil spots. I'm also keeping an eye out for leaks underneath the car all year around but never noticed anything.
It must have a small leak that has been going on for a very long time.
The gearbox is cleaned with carbcleaner now and I'll keep an eye out for leaks and keep an eye on the oil level.
I'm surprised the gearbox is still in one piece.

If you have lost ALL your gearbox oil I would expect the area to be covered in the stuff mixed with road dirt. You do not say that the area was particularly gungy so maybe the previous owner drained and forgot to refill it. has it had a recent clutch change?

Service book says clutch replacement april 2015 by a car repair shop.
The area in fact looks pretty gungy. I can only jack the car up so far so it's hard to inspect properly. Add to it that I'm paranoid about the idea of crawling under a vehicle,-I've had jack stands collapse on me before. Thank God it happened when I was sitting beside the car.
Earlier today when I refilled the gearbox I waited a few hours, then peeked underneath the box and it was dripping. I put a pan underneath and after that no more dripping.
I'll need to jack it up a decent height and support the car to make a proper inspection.

It can take a while for the level to settle if you over fill it a bit. I would be surprised that the gearbox has lasted this long if it has had no oil in since the clutch change in 2015 !!!!!!!