That 5 flashes code is "Flame sensed when no flame should be present."
Unplug the flame sensor and check with an ohmmeter set at the highest sensitivity range between the plug contact and cabinet ground.
Check the control board for any crud on it that might be bleeding the flame sense current to ground and causing the code.
Those are just grasping at a straw measures... if no joy, the most likely problem is a defective control board. Sorry.
Edit: one last thing to check... watch the burner flame that the detector rod is inserted in and see if it goes off immediately when the call for heat stops. I doubt you have a lazily closing gas valve but it has been known to happen and when it does, you get that same signal. Just another straw to grasp that may help to verify the failed device and not replace anything else unnecessarily.