I'm maintaining 2 - 5.3's. One with 103k (2000), and one with 73k (2004).
You can use just about anything in these engines.
I'd suggest anything that you know will be readily available locally, that fits your budget.
I'm using Rotella T5 synthetic blend 10w30 in the 103k engine, and Pennzoil Platinum 5w30 in the 73k engine, and changing every 6-9 months in both.
Main reason for running PP in the 2004, is because it has a short commute, and many times the engine is shut off before it reaches full operating temperature, especially in winter.
Both vehicles are used to tow as well.