Car quits after 3 to 5 miles

When the car stops, have you checked if there is spark when trying to start it. Check the coil, if it is defective it will get too hot and car will not start. Many of these cars also had a resistor that failed and made the car stop, check to see if your Chevy has one, it was usually located on the fire wall. My 1957 Ford Fairlane developed the same problem until I replaced the distributor with the electronic module. I don't think it has to do with the fuel system, but don't forget to replace the filter cartridge as well. Hope this helps.

Try swapping out the coil.