5.7L, 5.9L, those are 15 year old engine/trucks with 4-spd trans. Half ton tow ratings back then are borderline enough for 7200-ish pounds. Now if you are talking 2009+ when everyone has 6-spd trans, then it's more likely to be rated for the weight. The 3/4 ton base gas engine trucks with 3.73 axles from that era had 7-8k pound tow ratings.
But 7500 pound 5er means 1100-1800 pounds of pin weight. Add in a 200 pound receiver and people. Few half tons have that kind of payload, especially 15 year old ones with worn/sagging springs.
Find a 3/4 or 1-ton that is not abused. You'll be far happier.