My 99 5.0 did the same.  In my case, I had a fuel injector that was
leaking.  That flooded the cylinder with the bad injector, and also caused
the fuel system to lose pressure - so the other cylinders were not getting
enough  gas when you turned the key to start.  It took 2 to 7 seconds to
start and begin to smooth out the idle.

First, put some new plugs in if you haven't had new ones for awhile.  Read
your old plugs carefully. If you have a bad injector, the plug for that
cylinder will have heavy deposits on it. You will have seven good clean
plugs to compare it with, so it should be obvious.  Make sure you remember
what cylinder the bad plug comes from.

Also, while you are at it, clean your idle air control valve and your MAF.
There are plenty of instructions on the internet for that.  This helped out
starting, idling when cold, and generally made the truck run a littls
smoother in my case.

Hope that helps!

Post back if the above doesn't help.

If new plugs and the cleaning