Just because an ATX power supply can supply more current than you need doesn't mean it will. The whole point of a regulated power supply (such as an ATX power supply) is that it supplies a more-or-less constant voltage whatever the current demand from it, within limits.
Many ATX power supplies do give better regulation when they have a minimum load applied. So you might want to put a load on the +5V line (a 12V brake light bulb will probably do nicely).