I have a 84 Camaro and generally when I start it, it runs fine in idle, however, as soon as I start driving it about 5 minutes after the engine splutters and dies. Restarting then is almost impossible.

Carb'ed I'm guessing? If so, once it dies pull the aircleaner off, and open the throttle by hand and look into the throat of the carb, see if gas squirts. If no gas, narrows it down.