Well, it depends. In theory, an electronic device can only see the voltage difference between its inputs, so, yes, hooking up -5V and 0V to the GND and 5V inputs respectively will work, as will hooking up any voltage sources that have a value of X and X+5 respectively with respect to some arbitrary point you deem as "0V".
However, you have to be careful if the device electrically connects to other devices (even unintentionally, like their metal cases touching). If the power supply is non-isolated, its "0V" will not be entirely arbitrary, but rather connected directly to mains neutral. Thus, your device's "ground" will be -5V versus mains neutral. If you try to connect it to some other device that is itself powered by its own non-isolated power supply, and thus with a "ground" of 0V versus mains neutral, fireworks will result.