Truck will not stay running

How does it run for five seconds if a ground is missing?

If a ground wire to the frame and body is missing, you will not have exterior or interior lights as all of those circuits go to ground through the body, then back to the battery. That includes the starter solenoid, which is working. That ground wire is the smaller negative battery wire that is bolted to the body.

A better suspect is fuel pressure is dropping. I would start by connecting a fuel pressure gauge so you can see if I am right. You can also monitor the voltage on the fuel pump relay to verify it is staying on when the engine is running. One place to do that is on the double light blue/orange wire in the test connector. The voltage there is drawn down close to zero volts to turn the fuel pump relay on. If that voltage jumps up to twelve volts before the engine stalls, the fuel pump is turning off and is causing the stalling. The engine will run for a few seconds until the pressure in the line is depleted.

Yes. Well, possibly. If a fuel pump is failing, the truck will run on the other one, but more commonly, a signal goes missing from the crankshaft position sensor or the camshaft position sensor, then the engine computer sees that as the engine stopped rotating, so it turns the fuel pump relay off. That is done in case the stalling was due to a fuel line getting ruptured in a crash. Turning the fuel pumps off prevents them from pumping raw fuel onto the ground where it would be a major fire hazard.

All other manufacturers turn off power to the fuel pump and the injectors and ignition coils when one of those sensors fails, so the diagnosis starts with checking for loss of spark. Finding no spark is accompanied by no injector pulses about ninety five percent of the time. Ford does not do that. You will still have spark when on the other brands you would have a crank/no-start. Running for five seconds confuses the diagnosis. You are getting fuel pressure because the pump runs for about one second each time you turn on the ignition switch. It is supposed to resume running during cranking, but that does not happen when a sensor signal is missing.

The next problem is reading diagnostic fault codes yourself is harder on 1995 and older Fords than on any other brand. Even if you have a code reader, the process is painfully-slow, but that is where I would start. If there is no fault code to direct you to the circuit that needs to be diagnosed, you will need a scanner to view the sensor inputs and if one or both signals are missing.