5 blinks

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.

You can now be reasonably sure it's the control board.

There are 2 different boards that were used so get the info directly from the board to be sure you're getting the right one.

Edit: I assume you have tried leaving the power off for an hour or so just in case there is some phantom residual charge that is messing with the logic board. Slim chance but still a glimmer of hope.

FYI:

Flame Current Requirements
Minimum current to insure flame detection: 1 μa DC*
Maximum current for non-detection: 0.1 μa DC*
Maximum allowable leakage resistance: 100 M ohms
*Measured with a DC microammeter in the flame probe lead

I'd probably check the 2 electrolytic capacitors before giving up and ordering a new board. I have fixed a few boards with bad power supply filters. One of those caps can fail and cause an a/c component on the d/c supply voltage to the logic circuit and cause strange symptoms. I had a scope that could check that without removing the board. Without a scope, just replacing them outright is less than 5 bucks so worth a shot if you're comfortable doing that kind of work.