Your problem is very simple

Your X5 never had nav when it left the factory.

The nav has been retrofitted at some stage and is working perfectly.

HOWEVER: you have the LOW instrument cluster, which cannot deliver the necessary data that the nav wants (trip computer data, time, date etc) because the low cluster (low IKE) is not intended to be used with the nav. An X5 with factory nav ALWAYS has the high cluster (high IKE). Only the high IKE has all the data.
All the data that is not working - clock, date, trip computer, limit - is all held inside the instrument cluster and managed by the high instrument cluster. The nav is just a display and keyboard.

You only have two possible solutions to choose from:

1. Keep nav and replace current low instrument cluster with HIGH cluster then you have EVERYTHING working properly.

2. Keep cluster and replace nav with standard radio, and everything will work properly except you have no nav (but I wouldn't do this, would you?)

3. Leave as is :-)

I can show you a way to change the language into English as a work-around, which will likely work. To do this we take a standard OS disc, and replace the German text with English. The nav thinks it is German, but English will be displayed. But I recommend replacing the instrument cluster with the HIGH cluster.

An retrofit instruction exists for the E39, which is very similar to the E53 in terms of electronics. It's on the net, google for "retrofit high ike to E39" or similar and you'll find lots of info.
The high instrument cluster requires an adapter cable loom, and a new water level sensor in the radiator expansion chamber, a new expansion chamber, and then it has to be programmed to your car.