Follow the -5V wire back to the board and trace the track. It may go to a 7905 regulator as Claas suggested, or it may be supplied from a winding on the main transformer via a diode. Check for broken tracks, dry joints, and broken joints, and VERY CAREFULLY check the pin voltages on the 7905 if there is one.
Have a look at some general schematics for PC power supplies. You will be able to see how the -5V rail is generated.