Yes it should be rated to handle 5000 lbs. Especially on the flat land around where you live.

Years ago, I was hauling a load of horses up to a trail head in the Uintas of Northern Utah.  The climb from Evanston Wyo  @ 6500 foot elevation to the Highline Trail head at 10,000 foot is a pretty good work out for most rigs. It's posted as 60mph along that hiway, As I was driving I over took a 3H bumper pull trailer behind a Older Dodge pickup that was crawling along at 30 mph.  My diesel truck was moving at the speed limit so we easily passed him. At the trail head, he eventually pulled in and I was introduced to him as somebody joining our group for the weekend. I asked what engine and he replied that he had the 318ci engine. Which was Dodges small block comparable engine to Fords 302.

The point being, That he did make it to the trail head towing a 3h trailer with a 1/2 ton pickup and small block engine. He had to be patient and just grind up the hill, while my newer diesel just cruised on by.  As long as you recogize that you will occassionally be the bottle neck in traffic flow and are comfortable with that. The Ford F150 with the 302 will serve you well for a 2H Bumper pull.

I have a 1990 F150 4x4 with 302V8, manual 5 speed.  I used it to pull a steel 2H BP for years until I got 3H GN and bought a diesel 3/4 ton.

I still have the F150 302 and its still going strong with 250K on her. I did add a leaf to the rear springs and put heavy duty shocks on.

Drive carefully, make sure the brakes are in good shape, and you will be fine.