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If you have cleaned the flame sensor then there must be an issue with the connection of the flame sensor to the control board or the control board itself is bad and not recognizing the flame sensed signal. This is classic symptoms for false flame sensed if it is constantly lighting the burners and going out within this 5-7 seconds every time and then trying again 3 times then locking out.
You could try changing the flame sensor but more than likely there is a bad connection or the board is bad. Make sure the flame is spreading all the way to the end burner where the flame sensor is located
No you have to have that flame sensed signal and there is no way to trick the board because this is a millivolt signal and nothing else on the furnace uses millivolt so nowhere to rob this voltage from and send it to the board.
When there is not flame sensed signal at the control board about 10 secs after the board sends voltage to the gas valve then the signal to the gas valve is cut by the control board.
Many times I find that where this single wire leading from the flame sensor down to the board will be loose or broken at the coupling plugs it goes through on it's way to the board or even at the actual plug at the board. Giving these plugs a wiggle as the burners light will indicate to you if the connection is bad a lot of times.