If you are planing on using power supply, you can make it anything
you want but if you are planing on using single power source
like battery it all really depends on how accurate the -5V has to be.
Check the datasheet. Normally the negative voltage should
not be critical, it's only for contrast of the display so I would
not be surprised if it works with anything between -3 and -5V.
If you plan on powering your device from 9V battery, you might
try to use circuit bellow. It will give you regulated +5V.
The difference is the negative voltage Vneg=5V-Vbatt.
For example if your battery drops to 8.6V, negative voltage would
be Vneg=5-8.6=-3.6V. Check the datasheet and see if you are
lucky...