What's that noise?
 

My '04 X5 intermittently, has happened 2x in the last week, when comming to a ALMOST full stop then accelerating from the stop at moderate throttle pressure there is a loud noise/thud from the rear. The sound is like something slid and hit the back hatch.
I just bought this one owner X5 w/95K and it seems like one thing after another and this is after a clean bill of health from the local BMW dealer.

Sound like slack in the drivetrain. And u sure it's in the rear? Could be drive shaft slip, maybe worn diff bushings? Subframe bushings maybe?

It's happened twice in 500+/- miles, rest of the time runs great...well except for 2 previous posts, but these have nothing to do with driveability.
Coincidentally it happened at the exact same stop sign going different directions each time, weird??? Really.

Probably your rear end ball joints and control arm bushings need replacing. If they haven't been done they are probably due? Most "inspections" probably wouldn't reveal any of those being worn until you get thuds, etc. At least it did for both of my X5's.

Good Luck!

The noise was a broken motor mount. Replaced both and the noise is a distant memory.