The 27107504567 is from year 2000 up to 10/2003 for a E53 3.0, but not for a E53 4.4. So if you purchased a 27107504567 Transfer Case it is not compatible with a 4.4 X5 per Realoem. If you look at the picture you posted there is some physical difference between the two transfer cases.

Edit, it appears that the 27107504567 transfer case is for a X with a manual transmission, and since none of the V8 engine X came with a manual transmission it looks like this transfer case is for a 3.0 with the manual tranny.

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2006 Infiniti G35
2001 BMW 3.0I E53 X5 Build date 08/2000 SOLD
Lotus Europa 1970 Destroyed by fire
Lotus Europa 1970 S2 Renault Powered
Lotus Type 52 1970 Twincam Webers Powered
PORSCHE 911 Targa 1982 The Garage Queen
Audi Avant donated to Kars for Kids
BMW 525IT Sold
Audi 4000CS Quattro Sold
Jensen Healey Lotus Powered Sold
Opel 1900 Sold
Triumph Spitfire 1971 Sold
Triumph Spitfire 1968 Sold
Plymouth "Cuda" 340 Six pack SOLD