With a 5400 lbs base curb weight. Adding two passengers (300 lbs) and 200 lbs of misc stuff in the truck you're at 5,850 lbs. If the trailer loaded is 6,500 lbs you'll have approximate 780 lbs of tongue weight (12%) which brings the total to 6,680 lbs, short of your 7,300 lb GVWR.
Assuming proper weight distribution/sway control the truck should be able to tow with this set-up. How well it tows is somewhat subjective with the major issuing being the downshifting and higher engine revs as the grade of the road steepens.