I think I'm headed in the same direction (2008 X5 4.8i with 129k miles). My wife usually drives the car so she didn't really notice the sound under the hood was different. A whining/ whirring sound. As soon as I drove it I said when did it start doing that and I showed her. Revving the car in neutral/park and driving up to highway speeds it makes the noise. She said abot a week ago.
I thought it was the water pump so I ordered one (seemed to come from that area). I didn't change it for a few days since I didn't have all the right tools (torx bits, BMW loves using them) I went out got a set. In the meantime I thought maybe its the Vacuum pump/air pump which is right above the A/C Compressor. I took it apart cleaned, looked ok, cleaned it cleaned the CCV valves (had a bit of oil in the lines and valves), but the noiuse was still there. Finally today I decided to replace the waterpump. What a PIA! There is a hidden bolt BEHIND the Harmonic balancer. ALso to get the harmonic balancer you need to take out 8 torx bolts blindly by feel. a couple hours later and many bruises and scratches replaced it. The old once looked ok, the pully did not make any noise or look bad.
Now to get the harmonic balancer you need to take off the A/C belt, again PIA. Apparently it's a stretch belt and you need to crank the pulley while pulling the belt off. I couldn't do it so I figured take the harmonic balancer off and just pull off the belt. This worked.
Once the belt was off the A/C compressor I spun it and did hear it making a sound. At least it was much louder than any other pulleys. Most likely this is my issue, also noticed that A/C is blowing from Drivers side nice and cold but warm on Pass side. I had filled the system with refrigerant a couple months ago so most like the AC compressor is basically dying.
Getting the A/C belt onproved to be nearly impossible. until I noticed two bolts holing on the an accessory pulley next to the A/C compressor, I loosened those and it lowered the pulley enough to get slack to put the belt on The one bolt is on the front (no big deal) the SECOND one, it on the bottom and it's nearly impossible to get a an extension socket and torx bi in there. A lot of cursing later its all done but most likey an A/C compressor will be needed.
On the part you noted are you sure about the number?
I guess the one below also comes wotht he Cutch and coil assembly so its more expensive.
I see this:
2008 BMW X5 Parts -
COMPRESSOR X5; 4.8L
Include: Clutch And Coil Assy.
MSRP Core ? Save Online Price $1,419.89 $0.00 $293.92 $1,125.97