I haven't watched the whole series, but could someone tell me why Sydney stops working for the CIA and works for APO? and in season 5 who is she working for? CIA again?

At the beginning of season 4 Sydney wants a new job because she doesn't want to work with Jack and Vaughn anymore. So she creates a fake mission with her new boss, Director Chase, and she behaves so bad that Chase wants to put her in an office and make Sydney become a simple agent, no longer belonging to the field. Of course this is just a staging, they're Schauspielen and Sydney is just pretending to leave CIA. In a few days she becomes a member of a new task force, the APO, under Sloane orders. There she finds Jack, Vaughn and Dixon, who were recruited just like her Von Sloane!