A friend of mine has a 2000 Chevy pickup with the 5.3,and he was having difficulty getting it to start first thing in the morning,mostly when the temps were below 35 degrees out...
He replaced the fuel pump relay,fuel pump,and sending unit (gas gauge was not working all the time,so he did it while it was apart)..that failed to cure the hard starting/long cranking time problem though..once it started,it would fire up instantly the rest of the day as long as it did not sit more than 4-5 hours..however,as time went by,it started refusing to start on warm days too,and after not sitting long at all..
He also replaced a few sensors to no avail on the engine (coolant temp,and O2 sensors),and it wasn't until he was at a Chevy dealer buying some parts for another vehicle ,that he mentioned his problems to the parts guy,and he said "you should replace this harness--and he went and grabbed one off the shelf--he claimed many trucks were having the same trouble and this harness was found to be faulty"...
He bought it,it was about 35 bucks..it plugs in under the dash near the steering colum,I think it is part of the ignition switch harness...ever since he replaced that,it has fired up instantly regardless of the temperature...
So,you may want to look into that,as a possibility..