Regulating Negative Voltage
Assuming you want the ground of the load to be the same net as the ground of your input power source, it won't work. In your proposed circuit the regulator can only dump more or less current from a positive supply into the ground net. It doesn't have any way to control the current drawn from the load's negative terminal.

What you want is a negative linear regulator. LM7905 is a low-cost one for -5 V. LM337 is a low-cost adjustable output one.

You will also need an input power supply more negative than the voltage you want to apply to your load.