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I would guess lift pump is going bad, or injection pump.
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I would agree if the truck was a 98.5-2002 with the VP-44, but since it's an '05, the CP3 injection pump is less prone to failure. Also in '05 they went to an "in-tank" lift pump which is also "less" prone to failure (the are not fool proof but seem to be better than the filter mounted one)
I would guess cam\crank sensor, my '05 will miss about once every 2 months and usually throws a 606 and 336 code. Mine never completely dies it's just a studder that's caused by my TST powermaxCR box. The truck will run with one of those sensors unplugged but is dead without the other, but I can't remember which it is.