Shimano 105 brifters (5800) and Avid BB5 compatibility Are Shimano 105 brifters (5800) compatible with Avid BB5 mechanical disc brakes?

Yes they are. I had Avid BB5 calipers with Ultegra 6800 levers (same cable pull as 105 5800) on a Specialized Tricross and they worked very well together.