Welcome to one of the more enduring terms in use by X5 folk. FSR is the final stage resistor and it controls the blower motor on the cabin heating cooling system. It tends not to last too long and as it deteriorates the cabin blower becomes erratic, speeding and slowing for no apparent reason. The fun part happens after you turn off the car; often the blower stays on or comes on all by itself. By the time you next try the car the battery is flat. This becomes irritating. If you've never experienced it you're lucky.

Search this forum for FSR and battery drain problems you'll be amazed.