After the above tests are completed, take a look in the trunk to make sure it does not have the grave yard water floating around the battery. With all the electronics in there it can be the end of your review.
There multiple possibly causes, maybe a few at the same time. Many owners ignore 1-2-3 issues until the 4th one comes along and now it is time to make the big decision, bite the bullet and have the multiple repairs completed or bail pushing the problems to the next and final owner.
The vehicle you are looking at has lower than normal mileage but was un cared for. Why? Lack of driving reasons or something else?

On the list of potential causes
Ignition switch
Bad grounds
Wiring harness issues
Car was wrecked and never reassembled correctly
And on and on

Now the last point, offer $5k, AFTER a PPI. That step will save your bacon, if I can still use that term in today's snowflake world. Any competent bmw tech working in a well stocked Indy shop can do this for you

__________________

2005 X5 4.8IS
The Blue ones are always FASTER....

Current Garage:
2005 X5 4.8is
2002 M5 TiSilver
2003 525iT
1998 528i
Former Garage Stable Highlights
2004 325XiT Sport
1973 De Tomaso Pantera, L Model
1970 Dodge Challenger T/A 4 sp Alpine White
1970 Dodge Challenger T/A 4 sp GoManGo Green
1971 Dart Sport, “Dart Light” package
1969 Road Runner 383
1968 Ply Barracuda 340S FB Sea-foam Green