I'll be flying into DFW from overseas (with Qantas/AA, around 1PM), and my connecting flight is 5h 40m apart. Since the flight is international, I'll end up on the landside of the airport. Does it make sense to leave the airport before going through the security? Or am I better off just heading directly to the airside and spending the whole time there? If so, are there any interesting places in the airport?
After you've been through immigration and customs, there's a dedicated security checkpoint to get you back airside. In my experience at multiple airports (though I've not been through DFW), the queues at these checkpoints are short to non-existent. So while, technically, you are landside, in practical planning terms, you should think of it as being airside. In particular, if you do leave the airport, you'll have to return through the general security checkpoint used by everyone who's checking in and those are typically much slower.
So I would say that, rather than treating this as arriving landside at DFW, you should allow, say, an hour for getting through immigration and customs and ask yourself, "If this was a regular airside connection of 4.5 hours, would I go visit the city?" Bear in mind that you'll need to be back at least an hour before your connecting flight and, in practice, that means an hour and a half to allow for delays. So now you're down to three hours, in which time you have to travel to Dallas and back.