There is a recall on the E60 5 series regarding the rear light assemblies. Apparently the ground path for the lights is inadequate and the current flow corrodes the return path causing it to overheat and damage the wiring connector. There was a TSB out for it; then BMWNA issued a recall. You might be having the same problem; since the X5 was originally based on the 5 series platform.

I fixed it myself by riveting (you could also use a machine screw and locking nut) a new ground wire to the light frame and spliced it into the return ground wire; bypassing the connector. Worked like a champ, and that was exactly what the original TSB directed the technician to do as well...