Measure the 5V voltage across a logic chip on the PCB and not at the edge connector or PSU. Don't measure at the PSU because you need to take into account the resistance of the wires, the loom and the edge connector, and don't measure at the edge connector for the same reasons.
What you need to do is find a 74 series logic chip on the board. Then using this picture, put your probes on the pins marked. Your meter should be set to DC (a solid line with a dashed line above it) and in the range 0-10V or as near to that as you have available that is greater than 10V.
Note that I've marked the notch that the chip will have in grey pixels. This notch needs to be on the left and the chip orientated as per my photo. It doesn't matter which way round you have the probes as you'll still get the correct value, but it may show as minus voltage. That just means you've got the probes back to front and is not a problem.
Then for your 12v measurement, set the meter to DC again but the range to 0-240V or the nearest voltage setting (you may notice a pattern here - you always set your meter to a setting that is above what you're expecting and a little bit extra, just in case the power is higher than thought. You don't measure 5V on the 240V setting as you lose a degree of accuracy). This lists the JAMMA pinout but basically to measure 12V you need to put the black probe on pin1 of the JAMMA (it'll have black wires probably) and the red probe on the 6th pin. The actual value of the 12V line isn't super critical as the amplifiers are designed to run from perhaps 9V to 20V, which is why you're good to measure the 12V at the edge connector. The 5V needs to be much more precise which is why you measure across an IC.