You don't mention what year the 5er is, but I would look at the equalizer links if you have a leaf spring suspension. I had a blowout on my TT after many years of towing with no issues, and after getting new tires I was monitoring temps and the new tire in that position was running hot too.
Turns out the Trail-Air equalizer on that side was rusted and frozen in position. Since it couldn't pivot it wasn't allowing the weight on that side to be shared between F/R axles and was overloading the front tire.
Yes, running nose-high will put more weight on the rear trailer tires, but also check all suspension components (not just bearings) to be sure that everything is working as it should.