Actually, no need to buy any tool.
Go to your local Advance Auto Parts and RENT the tool (Bushing tool).

The E39 5-series and E53 X5 rear ball joints are the same.

I wrote a DIY Rear suspension Overhaul for E39 below and you can see the tool. You can rent a spring compressor at the same time and use the threaded rod with the bushing tool:

https://www.bimmerfest.com/forums/sh...d.php?t=545345

E39 & E53 ballpoints (part and procedure) are the same, but many have struggled with the generic rental bushing removal tool on the E53. I understand the flat spot on the receiver cup is quite important on the E53 to keep it straight. I have used he autozone tool on the E39, and struggled, and used the CTA tool on E53 and it was like
Child’s play

The key thing with rear ball joint:

1. Soak with PB Blaster, WD-40 one week ahead of time to allow the fluid to get in there.
There is likely salt in there making removal difficult.

2. When doing this job, I usually heat it up a bit, maybe 30 sec of heat.
It works well with Advance Auto Bushing rental tool.

I never understood this gravity method.
The last part of the tube has to go upwards into the fill hole,
so how does the fluid climb upwards into the fill hole?

ALWAYS buy the right tool for the job.

As long as the high end of the hose is higher than the fluid level, it flows.

I filled my diffs like this - at the rear I had a hose running out from the back of the car up to (and taped to) the trunk lid.

I used a fluid pump for the transfer case - the fluid is too expensive to risk pouring it all over the garage floor!!

Wow, great deal with 87K and working pixels on the MID? Definitely do the expansion tank, PS fluid, transfer case, and filters. Pull the covers and inspect brake lines. Get a diagnostic tool if you don’t already have one and reset the transfer case fluid change interval once complete

As luck would have it. I couldnt find my fan clutch tools. Found the wrench but not the holder for the hub. So I stopped with just the removal of the airbox and PS resivour....which of course needs a new hose to the cooler (good call guys).

Of course the local shops don't have one for sale and the rental are for domestic cars, and Amazon wont deliver till Saturday so I'm a bit dead in the water for now.

I'm going to be impatient and try and make the tool myself.
Found someone who posted a nice drawing of the holes
https://www.bimmerfest.com/forums/sh...d.php?t=254623

$2500 does seem like a good deal
Clean and low miles.

But, it seems neglected
But, issues don't seem big.

KBB private party would put him at $5000
Still a good deal, after he sorts it out for another $1000 (tires)