Negative voltage regulators
Simple answer:  You would get 5V in your case, but referenced to -12V instead of ground.  In other words, you would have -7V, not -5V.  In addition, the regulator would only source current onto the -7V rail, not sink it as would be expected for a negative voltage.

If you want to run some circuitry from 5V between -7V and -12V (the -12V will be the ground for this circuitry), then you can use a positive regulator as you described.  If however you want to run some circuitry between ground or higher and -5V, then you need the negative regulator.