Ok,I have spoken to the prior owner.
She is 100% on the car being 5 speed and it working with no issues (yes I did ask her if she meant 5 forward gears AND reverse

).
However, since the internet verdict is that it is 4 speed, and in order to answer many questions - I will take the end plate off IAW the BMW IPC, photograph the shaft & synchro's etc, replace with cork gasket / Thiokol, put fresh oil in and post pics.
That should answer questions on condition/gears/condition.