I am trying to build a simple adapter for a mini ATX power supply for a vintage mac, 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?
"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"
"I have a tiny 12 volt ATX power supply that has a 12v and 5v rail"
I don't know what do you intend to say when you used the expression "own separate ground". Why do you need a separate ground?
The table that you linked doesn't say anything about "separate ground":
According with those specs, the -5V is just a negative voltage, those -5V are measured in relation to the same "ground" 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.
You need to use a transformer-based 5v DC-DC converter. You power it from a +5V or +12v output, then you can tie its positive output to the PSU ground (since it is isolated with the transformer), and its negative becomes your -5v source.
Or (a simpler solution), if your ATX has a -12v source (which it should), use an LM7905 step-down to obtain the -5v source. But that will be 1A max.