You don't need anything fancy... That opamp has a 6V supply range. You can simply use a diode drop... use a 5V voltage regulator with it's ground node raised above the (now -650mV rail) by a diode drop.
The point where your diode meets the ground pin of the regulator is the "system ground reference", or "0" volts so the speak, or the point of the GND symbol. The other rail is now -650mv below ground.
see attached spice.