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Originally Posted by fotis
We have a travel trailer... the gvwr is 5400lbs.
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Average tongue weight with a wet and loaded trailer should be around 700 pounds. Add 100 pounds for a good weight-distributing hitch and your total hitch weight should be about 800 pounds.
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...Maximum tow capacity is 10400 lbs,
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That tells you your drivetrain has plenty of power and torque to drag that 5,400-pound TT over the mountain passes.
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...The weight of the truck ( I did on public scale) is 5820 lbs...the gvw of truck is 7000 lbs.
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If the weight of the truck included a full tank of gas and everybody and everything that will be in it when towing, then you have up to 1,720 pounds of payload capacity available for hitch weight. That's plenty of payload capacity for the 800 pounds hitch weight of your wet and loaded trailer.
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I have weight distribution hitch E2 round bar with 800 lbs maximum tongue weight 8000 lbs loaded trailer weight.
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That's the proper size WD hitch for that trailer. But the Fastway E2 is a relatively inexpensive hitch that is lacking in trailer sway control for severe sway-causing conditions. If you were my kid or grandkid, I would suggest you sell that hitch for whatever you can get for it, and buy a WD hitch with much-better sway control, that will cost you about twice the price of that E2.
Equal-I-Zer
Blue Ox SwayPro
Reese Strait-Line Trunnion with shank
Husky CenterLine HD (the old CenterLine, not the new TS)
Or for even a lot more money, a ProPride hitch that prevents sway.
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With that being said can I tow my trailer safely?
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Other than the questionable sway-control capability of your WD hitch, you're good to go with good margins of weight capacities. The biggest problem with most newbees is inadequate payload capacity of the tow vehicle to haul all the people and stuff in the truck, plus the wet and loaded hitch weight of the trailer.
Your WD hitch is probably adequate to control sway caused by about 95% of all towing conditions. What can get you upside down in the barrow ditch is a combination of slick wet pavement on a curvey road with a chug hole right in front of you that you cannot avoid because of the 18-wheeler meeting you at 70 MPH. Your trailer tires hit that chug hole just as the 18-wheeler blows past dragging lots of wind, and your trailer goes into a big uncontrollable sway. Yeah, that is a rare combo of conditions, but it has happened to me, other than the uncontrollable sway part. Thank goodness I had an expensive WD hitch that prevented the trailer sway, even under those rare conditions.
Welcome to IRV2! We're sure glad you joined the gang! 
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