Power Supply negative voltage as ground and ground
No, you can't still use the GND as ground if you want to also connect -5V to the device's ground. That would mean shorting -5V and ground rails.

But yes, you can power your device from -5 and 12V rails, assuming that your device haven't and doesn't need another grounding (e.g. a device which has an usb connection or some sort of other connection with the outside world). 

The GND from the Pc power supply will be grounded to the mains ground, so it's like it is an "absolute ground".

-5V rail from the ATX PSU will be at an "absolute -5V", if you then connect an usb cable which has it's grounding reffered to the mains ground you're basically shorting a -5V generator to ground. That's bad.

From now on, let's assume that you aren't going to connect anything else.

What you can do is take for example the -5V and make it your "new ground", now all the other voltages from that PSU will be shifted by those 5 volts.
So your -3.3 becomes -3.3 + 5 = +1.7V, your GND becomes 0+5V = 5V, the 3.3 becomes 8.3V and so on. 

In this configuration remeber that you can't exceed the -5V rated current