I have used Westley's Bleche White tire cleaner and it's the only thing that has worked for me to get the caked up residue off the rims. It definitely gets all the dirt off the tires and leaves them completely black and ready for some Shine products. just follow the cautions on the bottle and you should be alright as it's pretty strong stuff. Hasn't damaged my rims whatsoever! It's cheap too! $3 most places.
2008 535i - Alpine White - Cream Beige Interior - Lt Poplar- Sport Package - Premium Package - Comfort Access - iPod adapter