No. It is fine. Early ATX PSUs do have -5V and they work fine as soon as your AT to ATX adaptor has a wire for it.

What are good brands for early ATX PSUs?

Just my recent experience, I had my 386 mainboard even without any cards beside some vga, having problems after a while even showing signal to the vga output (darker screen until it became not visible) and things got back to normal with a AT psu. So I suppose the -5V rail or whatever difference there were with those AT psu, in some cases become a problem when using a more recent psu that in my case was an ATX one with the adapter but without the rail. I don't know maybe something was wrong with it but I powered a P4 3,2ghz after that test and it ran ok. So I'm going to use or an ATX good psu with -5v rail or a good AT psu. I'd use an ATX modern only if I knew being reviewed as safe for old stuff (voltage stability etc..) beside how low the wattage required would be, but with the rare adapter having the -5v generated on the cable with the regulator (I suppose).

You can also use a modern ATX PSU and create -5V from -12V line by using a simple voltage regulator. The power draw is small on negative lines. I've done at least once. Might be easier than dealing with old PSUs.

mpe wrote on 2020-06-16, 09:25:

You can also use a modern ATX PSU and create -5V from -12V line by using a simple voltage regulator. The power draw is small on negative lines. I've done at least once. Might be easier than dealing with old PSUs.

But I understand it need a minimal circuit (capacitors and resistor) to have a continuous load on it and I've yet to look into a schematics and values to build it. Sure it's not difficult and I'd have some idea of using a two digit display in a sort of mini-box inside the circuit to check the voltage when needed just to be sure to build something safe for the mainboard.