Arduino with 4 servos, a gyrosensor, a gps and a brushlessmotor

Can an Arduino uno handle servos, a gyrosensor, a gps and a brushlessmotor?

Yes, it can, you need some additional modules/controllers

Provided the brushless motor has an ESC then yes.

If you're trying to drive a brushless motor direct from the Uno then it's not really fast/powerful enough.

Steve