Powering a compressor for an air horn
Compressors, depending on design, can draw power in a way that results in surges during the compression cycle, so you may need a power supply capable of handling much, much more than the average current. You would need an oscilloscope and a shunt to measure the current draw during the cycle. 

As a wild-a** guess, I would say 20A @ 13.8VDC would be sufficient. 5A, probably not. 

The problem is that your bench supply will limit almost immediately (after the output capacitor discharges) once the maximum current has been exceeded. A car battery won't do that.