1993 Buick cuts off while driving and will not crank for 5 minutes. The car will easily restart after it has set for about 5 minutes but cuts off again after about 30 seconds. It does not run rough at any time. When it cuts off, the starter will not engage until the 5 minutes has passed.

This sounds like a problem with the ignition interlock system. This system uses a chip in the ignition key to tell the computer it is the right key in the ignition, and allows the starter to engage. If the key switch is worn out, or the key itself, the vibration from driving can jar the key in the ignition and cause the computer to shut the ignition off. If the key and switch are tight and have no play, there could be a glitch in the computer. You can have this checked by a good auto technician shop. GOODLUCK!