This Towing Guide to get you pretty close. It's for 99's but they should be the same.
Looks like the trailer rating is 7500 lbs max.
The issue is the 350 chevy. To put it in perspective that truck has 30 less HP and 5 lb ft of TQ than the 2014 4.3 chevy V6 base motor in the new silverado.
It's a great motor, just underpowered by today's standards.
IMHO, spring for the 454. You get 10,000 lb tow rating and plenty of power from a gasser. Plus the mpg shouldn't be that different between the 454 and the 350.
Thanks and good luck!
Jeremiah