I have had BGS tool for many years and I think it has been working 10+ times, so can recommend that. Has the flat section too.

e39 ball joint tool
https://www.amazon.com/CTA-Tools-869...ef_=ast_sto_dp

Notice the flat section? Now you can do e53 X5 too

That flat section is very important. It is why universal ball joint tools won't work on the e53.

I always laugh when First time DIYers try to use the universal tools rent/buy then complain about the process that anyone using the right tool find easy.
With the right tool the process is simple

I was a victim of a first time DIY on my e38 so bought the correct tool for my e53 and it was night and day difference of the experience removing those rear ball joints.

Can I go wrong for $35??

https://www.amazon.com/BTSHUB-Bushin.../dp/B09CCV1VGQ

It looks like it has the flat spot you need to be able to remove the e53 rear ball joint. The universal ones don't work for that reason. And, it's Amazon, if it doesn't work you can return it for free.

This is the OE tool with the flat spot to clear the rear suspension arm on the E53
CTA Tools 8692 Bushing Remover/Installer Kit