[Orangejbird]

Paxton Patterson that was hooked up to a Apple IIe
5 pin round (din?) plugs to motors.
What's needed to make this work with a PC USB port?

[Orangejbird]

Bump
Still looking for a solution. Convert to usb or use parallel connector?
Controllers? arduino gecko . . .?
Software?

[123CNC]

Apple IIe, where did you get that, Smithsonian or an archaeological dig in your area?

Best solution will be to look at thinks in this decade. Determine if your motors are stepper or servo, likely stepper. Determine your stepper phase, unipolar, bipolar, 5-phase, etc. If 8 wire, 6 wire, or 4 wire, you will have a lot of choices.

With no power, turning the handwheels for the cross feed or longitudinal or z feed, you should feel a cogging effect if they are steppers.

The Arduino route is fairly limited in power to drivers and steppers, generally speaking in what is widely available. But may work in your case, if you do indeed have steppers. From the picture look like they may be NEMA 23, maybe 34, but definitely short and likely low power. Try to find any labels or maufacturer markings on the motors or the motor drive boards.

If steppers, and once you know their inductance, a Gecko G540 might be a good choice. You could then also consider Mach 3 or 4, LinuxCNC, or Dynamotion or others. LinuxCNC is free and a great place to start or Mach 3 is also free for less than 500 lines of g-code.

[123CNC]

Also try a search for Paxton Patterson CNC Lathe on this forum (as well as others), looks like a few others have already made this journey.

[Fastest1]

Looks like a Sherline to me. Though there might be 5 pins on the plug, most likely only 4 are being used. Those are old round steppers. Not very powerful but good enough to get everything else in place first if budget is of concern.
Look into the G540, Leadshine MX3660, Hobby CNC Pro etc. All would work just fine.