if that backhoe has a loader.. get a 20' trailer. if no loader.. 18' is what I would reccomend. 16' would likely work.. but be a tight fit.. and may not ( probably won't ) let you get tounge weight orrect.
if you have a GN ball.. don't be afraid to get a 24' GN traler and drive in luxory.
a 16' trailer and that f250 for a N or 00/small 000 is fine..
having more is almost always better.. thus the 18' rec.
5k payload means you are right onthe edge of a 7k trailer.. however.. most 7k trailers will be abound 2kweight and that is 16'. going 18 and you are on the edge.. thus i reccomend a 10k trailer ( if gn.. go 14k )
ps.. you will be getting a tandem axle.. not single.. and make sure yours is legal per brake requirements of your state. most now want all axles braked. some allow 1.
you will also need a brake controller. . if your truck is wired for 7 pin already.. you are pretty much there, though you may have to put in a couple relays under the hood. your ford is new enough that you can hit a walmart and buy the plug for under the dash.. plug it in, and then plug in a brake controller.
if you are only wired for a 4 pin flat, then you need to run a couple more wires. 1, power wire from brake controller for brakes. and also a breakered or maxi fused line for power tot he 7 pin. both of those can easilly be run downt he rail of the truck with some zip ties.. the 14awg trailer wire packs is fine for this.. double insulated usually. find the 4 flat and union your 7 pin onto it.. that way you have both.
your f250 is a fine truck for the load.
one question.. i read 7.3 and 250 and just assumed a 7.3 psd and since you said auto, that would mean 95.5 or later.
is that what it is.. or is it the 93.5-94.5 7.3IDI w/ATS turbo? or the previous? 89-93.5 NA 7.3?
all will have the guts to pull an 18-20' 10k trailer... the 7.3NA might take a lil while to get up to steam on the interstate.. but will make it. the 7.3 turbo and the 7.3 PSD will be fine even at interstate speeds.
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