'98 sierra, k1500, 5.7 won't start until cold crank for 15 seconds

check for spark.. if no spark replace autoshutoff relay it controlls fuel and fire..

Testing of the fuel and ignition systems is in order. Intermittent problems need testing when the problem is present, otherwise it won't help find the problem.
I would start by checking for spark on a spark plug wire (or two or three plug wires, in case it may be a bad coil), during those times when it won't start. You need to see a blue, snapping spark to verify ignition system is working.
To check the fuel system, have the fuel pressure checked, and the injector circuit checked. Good that you hear the pump, but you don't know if fuel pressure is correct, or if fuel is getting into the cylinders. One short test is to spray starting fluid or carb cleaner into the intake while engine is cranking. If engine fires up for a few seconds, you know it is a gas related problem.
If ignition system is the intermittent problem, could be failing coil or coils, ignition module, crank position sensor, even the computer, or a wiring problem like a bad connection. Testing of each component will be required, or you could start throwing new parts at it, like many people do, until you find the bad part. Find a reputable mechanic-there still are a few, lol.

I would check the fuel pump relay first. You should have some fuel pressure in the lines when you turn the key on. The relay is powered for 3 seconds to boost pressure until the engine starts.
The relay may not be working or the check valve in the pump may be letting fuel back into the tank which would cause the pressure to drop to zero when the engine is off. You should have at least 15psi with a TBI system and 35psi with MFI.

The first thing I would check is fuel pressure. This type of fuel injection requires a minimum fuel pressure in order to operate. If fuel pressure is as little as one psi below minimum the vehicle will not start. You can try squirting a couple of shots of carb spray into the air snorkel while somebody cranks the engine over. If the engine starts and then dies you now you fpdeffinetely have a fuel issue. If the engine still won't start check for spark. Let me know what you find. Let me know if you have any questions and I'll do my best to answer them. Thank you for using FixYa.com!

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It sure could be. But, first...by "won't turn over" you do mean it cranks at normal speed but won't start?
A simple test of the fuel pump is to stand by tank and listen as someone turns key to on. When first turned to on, your pump will activate for 2 or 3 seconds, pressurizing the fuel system, and then shut off if the engine computer doesn't get a cranking signal. Do you hear it come on? If not, then something's not turning your pump on. If you can hear it buzz on briefly, then maybe it's your filter. Another test: Spray a little starting fluid into your intake manifold (remove the big hose going into intake manifold) while someone tries starting it.If it doesn't fire and try to stay running, then it's probably an ignition problem. But if it does fire off, then you know it's a fuel problem-likely your pump or filter. good luck.

You should not see any voltage after the 2-second prime until you actually start cranking the engine. If you don't see power on the grey wire when cranking, try jumpering across the fuel pump relay terminals

Did you do a tune up on the vechicle? Does it sound like it wants to start? It could be the spark plugs.

It could be that you have picked up a batch of dirty fuel that has clogged the gauze input filter that is part of the fuel pump inside the fuel tank.

I'n not sure what engine you have in this but some of these needed 60 + psi of fuel pressure to start when the engine was cool or cold. If it had only 59 psi they would crank and crank but never fire and run however they would get just enough fuel to act sort of flooded for a few seconds once they did start. A bit of external fuel and Bingo, they would start and run all day...until they sat for several hours again then the whole process was repeated. I would start by verifying your fuel pressure and go from there. If you find less than 60 psi when cranking then you most likely have a fuel pump that's just a bit weak. OEM pumps work best on this one if you ever have to replace it.

02 sierra 1500 5.3 starts very quick when cold but when hot cranks a lot before starting,I replaced fuel pump and filter did not help.It has 55 psi fuel pressure but falls below 40 kinda fast.???