The different diameter tires front to rear is most likely your culprit now that I see the tire sizes that you're running. However, I would suspect the different tire diameters to cause transfer case problem on an AWD system. But then again, the weakest link in the drive train will fail given enough stress placed on it.

If it was me, I would start by putting the same tire size on all 4 corners. Then troubleshoot from there.

I didn't have any issues before the oil/filter change - just after using an aftermarket one did I ran into shifting issue. Going back to the OE BMW filter solved my problem.

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2004 X5 3.0i
Born 02/04
Delivered 03/04