The dealer said that 5,000 - 10,000 miles per set of tyres was normal here, and a neighbour of ours agreed.
As little as 5000 miles on a set of tires?
You must be joking. According to my notebook, I bought a new set of Pirelli radials for my Bronco II in October 2006. So far they've done about 4000 miles, including regular driving over rough unmade roads every time I go in and out, and the tread isn't down much from that on the so-far-unused spare.
You could question whether the road surfaces have an effect, but when I was running older U.S. cars here I tended to use American-made BF Goodrich tires, and they would do 20,000 miles and still have some life left in them.
Rotate the tires!? That puzzles everyone here that I mention it too.
It always used to be done here, and I still do it. For some reason it seems to have fallen out of favor, but if you look in the manuals for old (1960s/70s or earlier) British cars you'll see the recommended rotation arrangement (different for radials and crossply).
I get some kind of response like since cars are so much more computerized you can't just rotate your tires. There are specific ones for each wheel or it will throw the tire sensor off (if you have one of those computerized tire sensors on your dashboard).
Tire sensor?
The only thing remotely resembling that I've ever heard of on some newer cars is a remote pressure sensor which will give an alarm if the air pressure in the tire drops too low, and even that is rare.
There's absolutely no reason why rotating the tires would interfere with any onboard computer systems.