If your e53 is prior to the "xdrive system" (Clutch Packs) then the Transfer case takes ATF ~.5L and diffs 75w-90 ~1.4L (rear), ~.7L (front). I used Red Line Oil D4 ATF and 75w-90. Fill till fluid comes out the fill whole in all three applications.

If it has xdrive, then use BMW fluids from the dealer.

k