2005 E53 Clunk from rear end??

[E533.0i]

Hello to all,I'm new to bmws for the most part.I recently purchased a 2005 e53 x5 with the 3.0i engine and automatic transmission.I got the car cheap because It needed a rear diff.Which was surprising considering the car only has 82k miles on it.Now I put in a rebuilt rear diff.My wife has been driving the car for the past 2 or 3 months.This is her daily driver.I drove the car recently and noticed that shifting into reverse and giving it throttle there is a clunk.My driveway is on a hill.So then the load change.Once backed up and shifting into drive and giving it throttle another clunk.

It seems as though when the load change occurs I hear a clunk definitely from the rear of the car.This only happens on inclines or sloped surfaces.The last time is happened the 4x4 light came on and stayed on.

I am a master tech by trade and have been working for audi for the past 12 years.I havent had the chance to inspect the car since I heard the noise.But Im just curious if anyone has experienced any other problems beside the rear diff??

It is possible the rebuilt rear diff is no good.But I would assume it would do it all the time??Another possibility is the transfer case??Or chain possibly??But then I would hear that from the center of the car and I would assume I would have abs and brake lights lit on the instrument cluster??I was able to pull codes recently but the scan tool I was using was very limited.Just told me the codes not very detailed.

Engine:
P111F Intake Air Temperature Sensor 1 Minimum Temperature Implausible (Bank 1)

Not really concerned with this one we'll see if it comes back.

P3199 Engine Coolant Temperature Signal Stuck

Possibly faulty coolant temp switch??

The engine fault i'll address if they return.As they were pending.

I had 4 fault stored I believe in the transmission.

Transmission/DSC faults:

5EB1 Steering-angle sensor, supply
Posssibly lost signal??or faulty steering angle sensor i heard is common??

5DD2 - DSC: Control unit, overvoltage
Not sure on this one if its related to the 4x4 light on not given the faults below.

5F42 - Transmission control Limp mode operation
I am not sure if i cleared all the faults after the original diff failed.Possible it an old fault.Not really sure.

5DEC -Also could be an old fault not sure.Ill have to check if it returns.However could be related to VTG motor or wrong rear diff the car??

55C4 - I saw a TSB that says its possible the transfer case is fault if this fault code is stored.I guess I'll have to recheck and possibly pick up a factory level scanner.






Just looking to see what else could be the issue besides the obvious faulty rebuilt rear diff.