Hi m5james,
The problem is ,you have facelift 04+ tail lights and the pin positions are different to the pre-facelift or your 01 X5.
All you need to do is this-
Pins to swap when fitting 2004-06 Tail lights in pre-facelit X5-E53 (1999-2003)

RIGHT TAIL LIGHT
6 TO 4

LEFT TAIL LIGHT
1 TO 3

If you need any pics or more info ,let me know.I do this all the time in clients cars...no need to buy the OE cable adaptors