How to create an ATX -5 volt rail for vintage Macintosh
&quot;I need a 5 volt rail that has it’s own separate ground (+5 volts to -5 volts) how would I go about doing this&quot;
&quot;I have a tiny 12 volt ATX power supply that has a 12v and 5v rail&quot;
I don't know what do you intend to say when you used the expression &quot;own separate ground&quot;. Why do you need a separate ground?
The table that you linked doesn't say anything about &quot;separate ground&quot;:

According with those specs, the -5V is just a negative voltage, those -5V are measured in relation to the same &quot;ground&quot; of +5V and +12V.
If you connect a voltmeter between -5 V and +12 V pins of this PSU, you would find +17 V; accordingly, the reading between -5 V and +5 V pins of this PSU should be +10 V.
If you have an ATX PSU, your easiest option is using ATX's 12 V and 5 V, and, as you need -5 V too, using a negative linear regulator (the most common is 7905) to convert the -12 V from the ATX PSU (blue) to the -5 V that you need.
ATX PSU's doesn't have -5V output, but ATX standard requires a -12 V output, and you will convert those -12V to -5V using a negative voltage regulator as 7905 IC (79xx IC regulators are the negative cousins of 78xx positive regulators).
Usually the -5V current requirements are low, that's the reason why a linear regulator as 7905 can do the job.
Maybe you will need to do some googling in order to learn about the negative regulator; but it's not complicated.