If you do a search on the work light power supply you should find an explanation on where to dig into the the wiring harness in the rear of BX tractors. On the BX2370 there will be three wires; one is ground, one is the work light supply and is fed by a 20 amp breaker, and one is an extension of the power supply below the seat and is fed by a 10 amp breaker. Five amps should not be a problem.
I forgot the 20 amp work light circuit is on all the time, not switched by the ignition. The 10 amp power outlet circuit is not on all the time as it is controlled by the ignition switch.