Light switch with five wires controlled by two circuit breakers: What is this?
It looks like you have an improperly wired accidental ring circuit. 

One of those switch terminals, the hot one,  has two wires on it because it is part of a daisy chain of such loads. (The other terminal has two load wires because they each run to several lamps, probably arranged in two daisy chains.)

A daisy chain of loads is acceptable practice, but your chain is improperly connected at both ends, to separate breakers. This violates code and common sense, and makes the wiring easily overloaded and unsafe to work on.

The fix is mechanically simple -- you just disconnect a hot wire from a terminal screw and cap it off with a wire nut -- but you should first decide where to divide the chain. This means identifying everything on the chain, so you can split it roughly in the middle leaving similar loads on each breaker. 

EDIT: Well, almost that simple. As @Harper points out, the neutral half of the ring must also be disconnected at the same place where the hot wire is disconnected. So you have two wires to cap off with wire nuts. Just make sure that all the loads powered by one breaker share the same neutral.