Not to derail but to add another possibility...
up to 09/98 e39 540i came with an air cooler for the transmission
17221740798 with frame 17111740796
Attach that to the E39 540i / m5 CSF radiator 7064
Buy the inlet and outlet hoses for the pre 09/98 auto e39 & splice them into the existing transmission cooler lines on the x5

No welding, no mess, no modification to the radiator etc. Even if that OEM transmission cooler is meh in regards to performance it's better than the engine temp cooler we currently have...

I have a fan delete in mine so I know I have the space for the bracket & cooler off the back of the radiator.