Save My Camera! (FPC Breakout?)
wires 1-2 and 5 look to be broken, so they will have to be repaired, if its just button contacts you can likely get away with conductive expoxy laid down in very thin lines, wont be easy, but should be possible

as for how you would connect your wires, I would recommend attacking the switch, as it will have bigger pins that are soldered to the flex pcb, you may also find your camera already has some interface on it to act as a trigger, change modes, etc, you would just need to determine what it is for your particular brand.