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I pull a heavier camper with a 2001 Expedition and a 99 F150 both with the 5.4. I do have the equalizer hitch, wouldn't even think of it without. When pulling in hills or into a strong headwind it works it pretty hard, but once I get up to speed it rolls along great.
Make sure your trailer has brakes on it.
Hey try this app, it has all the towing ratings you are ever going to need, plus it comes straight from the vehicle manufacturer too. Yours is in here:
Look in the 03 owner manual at pages 167/168 for the listing that matches your truck for motor size, gear ratio, and tire size/diameter.
Listed is the Gross Combined Weight (GCWR) you may not exceed 'regardless' of trailer weight.
Good luck.