For the LS3 for MY08, its 5.5 qts for base and 6.0-qt for Z51. The extra half quart is for the coolers.
I love these "oil reps".

Their job is to sell oil. Imagine if he can get you to run 15W50 at the track then throw it away when you get home. The bastards!
Ok, to the issue at hand: your LS3 will have the best durability with 10W30 not 5W30. You can get Mobil 1 10W30 at Costco.
For racing, whether you go with 10W30 or 15W50 depends on the engine, the driver and the weather. If your car has Z51 and the coolers, 10W30 is likely all you need for track days unless you're the type who always runs near the rev limiter and the weather is really hot. In that sitch, I'd use Mobil 1 High-Mileage 10W40. It's got only 1000 PPM phos and splits the difference in phos and vis. between 10W30 and 15W50. Amazing this Mobil 1 "rep" didn't tell you that.
If you don't have the coolers and you see sustained oil temps over 250°F, you can go to 15W50. The part about cats failing in short order is BS. Yes, 15W50 has more phosphorous in it than 5W30 but it's only 1200 ppm vs 800 ppm. 15W50 may decrease cat life over a long period of time but it's more likely the difference between 75,000 miles and 150,000 miles rather than failure in short order.
For more accurate info on M1 products see this
web page
I should add that the oil I've used for the last 20 years has a phosphorous content of 1100-1200 ppm and I have cats on two vehicles which both have gone 125,000 miles so far. I had another, scrapped back in 01, which had 140,000 miles on the original cat using that oil with 1100-1200 ppm phos.