The IRF540 is an n-channel device. This requires the gate to be brought higher than the source to turn on. What’s happening instead is that the FET is following the gate voltage, minus the threshold voltage. So if the n-FET gate is at 5V, and threshold is 2V, then it won’t conduct if the drain is higher than (5V-2V), or 3V. So it swings to that and pinches off.
Instead, use a p-FET, which switches on when the gate is lower than the source. Gate at GND, FET is fully on, gate at 5V, FET is fully off. The AO3401A is a 4A device that would work fine for this.