Get the trailer, a quality WD hitch with sway control, ditto on the brake controller, just do it. The rig will tell you what up-grades are needed.
Chances are your 5210 will hit the 7300 with astounding speed. Don't rely on the published weights, they are notoriously light, especially the tongue weights.
Get to the scales ASAP. And don't overlook the TV payload, axle ratings and tires.
Common cents is your ally.
"Sticks & stones can break your bones...and hail will dent your Airstream"
So when is this..."old enough to know better" supposed to kick in?