The most likely cause of a low oil pressure issue in a 5.3 is a blocked oil pressure unit screen or an oil pump o-ring failure. HOWEVER - there is an often overlooked and very common issue that puts many of these engines in the junkyard FOR NO REASON. It is a weak or failing oil pressure relief valve inside of the oil pan. If ALL of the above does not fix the oil pressure issue - it IS the relief valve inside of the oil pan. The spring wears out in these valves, which causes oil to simply dump into the pan - and not feed the upper part of the lifter feed circuit. The oil pressure sending unit is located in this circuit - which is the reason you get a low oil pressure indication - when in fact oil pressure is good. The fix is to either replace this valve, or to simply install a plug so the oil does not dump into the pan.... When you block this off - oil pressure will be better than before....