I have a 2001 Ram 1500 QC 4X2 with the 5.9L engine.  I pull a 3800lb dry
trailer.  It's close to 5,000lbs loaded.  It tows quite well but is slow
up the grades.  Previously I had a 2000 Ram 1500 with the 5.2L.  It
struggled to pull the same trailer.  Even on flat highways it had
trouble maintaining 60mph while towing out of OD.  I can't imagine
trying to pull 5,000lbs with the 4.7L especially the heavier 4X4.  If
you live where it's flat like Kansas you might do ok albeit rather slow.

    I used to drive a '91 ram, 5.2, 5 speed, 3.55 rear.  no tow package.  I towed
with it occasionally.  I loaded a '66 Mustang on a U-Haul trailer (about 5500#) and
towed it from MA to CO.  Since I didn't have the tow package, I used the bumper and
tap-a-lites.  Not a problem at all.  Truck towed it without any problems at all.
Couldn't use 5th very much, but that's OK.
    With your truck, I wouldn't hesitate to tow a 6,000# trailer.  It's a Dodge, and
that's what it was built for. It won't tow fast, and it won't tow quick.  But it will
get you there without fuss.  Since you already have the tow package, all you need to
add is a brake controller.  If you're traveling in high heat regularly (>100*), you
might consider an additional trans cooler.  Otherwise, don't sweat it.  Just hook it
up and go.
     Anybody who says it won't work, just doesn't know dodge trucks very well.

     The Dakota I have now will easily tow a 5,000# trailer at high altitude. It
makes a little more torque than yours, but not much.  And it is a little lighter than
yours, but not by much.

You have 2 considerations, IMHO:

Safety.. I think you're good to go, using an weight distributing hitch...
You want to be at LEAST 10% under max tow weight for safety, which you will be
if the trailer or truck aren't overloaded..

Fun... We pull a travel trailer that's 4,800# empty.. I'm guessing it's under
6,000# loaded... we have a 99 ram QQ 2wd with 5.9L gas, auto & 3.55 gears...
Grades are slow, but that's towing, IMO.. a Cummins would be nice, but we're not
going to trade up to a $40,000 truck unless we get a bigger trailer...
On level ground with OD locked out, it's a breeze to pull at whatever speed you
feel is safe... on a trip from CA to WA, we took some major grades at about 40 -
45 mph at maybe 3,500 rpm...

I think that a 5th wheel is a great idea... better weight distribution, less
total length, better ride and handling.... I'd put a good set of air bags on the
rear to help level the load and soften the ride..

The 4.7L has less torque than the 5.9, but I think it will do fine with a little
patience.. IMO, if it's a "Recreation Vehicle", you don't need to be in a hurry,
relax and enjoy the trip... YMMV

mac

Please remove splinters before emailing

The verdict is in...

I didn't buy the 5th wheel, but did pick up a 25' travel trailer at
4400 lbs dry.  We loaded it lightly- probably just barely over 5000
lbs.

As some of the posters predicted, it's pretty slow up steep grades (7%)
at high altitude (7000+ feet); we drop down to about 35 mph.  But there
are turnouts so we can get out of other people's way, and- what's the
hurry?

Where the grade is not so steep, it isn't hard to keep the speed up,
but you can only go so fast with a 25' trailer behind you anyway if
there are any curves in the road.

I did follow Mac's advice and got a weight distribution hitch, which
seems to steady things quite a bit.

On the other hand, we are beginning to look longingly at a 2500 with
the Cummins, which might be nice for added confidence on cross-country
trips and would open things up in the future for a larger RV.  :)

Thanks again to all who responded...