I'd pull it shouldn't be a problem with a f150.

 

I think an F150 is perfectly capable of towing it, but if it were me, I wouldn't do it with my truck. This would be a time when I'd ask my brother if I could borrow his V10 F250....

 

With your oversized tires, 4.56 gears would be good. Changing gears will cost $1200-1500. You don't want to do it twice. The limiting factor will be your payload. You have about 1600 pounds to play with. Take out yourself, any other passengers, camping cargo, firewood, etc and you could be down to 800 pounds for tounge weight. Check out the hitch weight of the trailer you are considering as toy haulers tend to be on the higher end to even out when the toys are loaded in the back.

You really can't find any trailer you like that has a dry weight of 5000 pounds? You only need to carry two bikes. Do they fit in the bed of your truck? That would keep you out of the TH models and the weight down a lot.

 

I have towed 7k with mine which is about what it is rated, it handled it fine. Left it in drive and didn't set any speed records but held the speed limit great. If it was level I could have ran in od but those pesky hills wouldn't let me. Mine is the wimpiest 5.4 setup you can get, I have the AODE trans and 3.31 gears with 255 tires in place of the stock 235's. Trailer brakes are a must though, you can do it without but it is night and day with them. It was a old tractor on a flatbed, not a enclosed trailer, that probably makes a difference too.

I pull a 1800lb car trailer with a 5000lb tractor, I would think you could find something lighter for a couple bikes.

 

I've pulled:

Bronco 5600# (full of fuel and parts)
Trailer 2000# (+ or - some, a real all metal one)
Peeps 600#
Misc crap 150#

All in all about 8000-8500. My F150 pull it without a problem. 4.5 hours each way. Even while pulling in the hills going to Big Bear.

My truck (2006 SC 4x4) is rated for 8200 or 9200 don't recall. And I put bigger tires on also. Pulling was not a problem. Stopping needed to be planned and started early.

If I was doing pulls like this alot, I'd get a F250 But for a few times a year I'll keep my F150

 

Any vehicle on a car hauler is still a lot less aero drag than a travel trailer.