For the actuator gear try to listen if you can hear a clicking sound when you shut the engine off like in this video. 2005 BMW X5 TRANSFER CASE ACTUATOR - YouTube

Mine was shot , replaced it with this :BMW E53 X5 N62 4.8L Search SiteSearch Actuator Gear

Still had some problem with the 4x4 and had the angle sensor fault. It was re calibrated and everything fine now.

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His : 2005 X5 4.8is (SOLD)
Hers: 2007 X5 3.0si (SOLD)
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Retired:
1999 518
2000 323i
2002 M3 (beautiful car)
2003 330Ci