Cranks over will not stay running

Will not crank anymore, as in the starter will not crank the engine over or do you mean that the engine will not start?

At first you said five minutes, now you changed your mind and say three to five seconds. Which is it?
Is there any security or anti-theft on this vehicle and if so is there are security or theft lights or messages on or flashing?

You never answered why you changed from five minutes to three to five seconds.
Fixd you would only need if an obdII. I think this is an ODDI. If the diagnostic connector has 16 pins that it is OBDII but if only 12, it is still an OBDI. Around 1994-1995 was right when they switched over.

That sounds like it could be a security problem shutting down the engine. Try a spare key or if you don't have a spare key clean that key where the chip is and try again.

If there is a security or theft light on or flashing, you will have to have the trouble codes retrieved to find out why the security or theft light is on.
If no security or theft light, then you should still retrieve the trouble codes anyhow. If this is an OBDI with a 12 pin diagnostic link connector, then there won't be many trouble codes at all to help diagnose this, but if it is OBDII with a 16 pin dlc, maybe so cause it stores a lot more codes that could tell us something. Let me know which it has cause this is right around the year 1994-95 where they switched over from OBDI to OBDII. OBDII and most OBDI has the dlc under the dash right where your right knee would be when sitting in the drivers seat.