The 5000 (gross)/500 (tongue) lb. rating is the maximum rating when towing without weight distribution bars. The 10,000 (gross)/1,000 (tongue) lb. the maximum rating when towing with properly adjusted weight distribution bars.
Using your numbers, looks like your trailer will weigh almost 6000 lbs. loaded. If you load the trailer properly, your tongue weight should be approx. 600-900 lbs.
Although you can use the Curt 14,000 (gross)/1,400 (tongue) lb. weight distribution bars, it's gonna be a bit "stiff" during use. 600-900 lbs. of tongue weight is not going to be enough weight to get the 1,400 lb. bars into their nominal operational range. I'd try to get one rated for 600-800 lbs. or 800-1000 lbs. of tongue weight to give you a more fluid range of adjustment and operation.