Amsoil Severe Gear Fluid - 75W90 and 75W110.
For the E53 platform, OEM spec is 75W90 for all makes up till 2003 builds.
Not quite sure about X-Drive variants.

I personally have ran 75W110 as I was towing and wanted the slightly higher viscosity.

Just trying to clear some shelf space. 5 qts of 75W90 available. 3 qts of 75W110 available.

A DIY differential will require just 2 qts.

Each qt is $11 each and shipping for any qty will be a flat $5 within the con us.