Then in lieu of any other potential symptoms, I'd say you for sure experienced the DDW's (Dreaded Death Wobbles).
If it's a bad tire, then you're likely to experience it again, especially under the same exact circumstances (same stretch of road at the same speed in other words) until it's fixed.
I don't know how low your gearing is, but even an '05 with 31's could be lugging in 5th at that speed. Unless it's a Rubicon with the 4.11 gears, you could have something else. I'm sorry I forget what gear ratios were available in '05, so I could be completely off here, but I agree with the others that suggested a lower gear going up hill at 50 to 55 mph.
What rpm did your tachometer say you were running at that time. Even though inline-6 engines are known for their low-end torque, that doesn't mean they like to lug down under the wrong circumstances any more than any other engine would. And they can also be revved up without damage a lot more than people think, or are led to believe.
Doesn't mean I'm telling you to over-rev it, but on a hill is no time to lug it down. Your rev's could easily make mincemeat out of a hill if they're kept over 2500 to 3000. And no harm to the engine.
Anyway, plenty of things could have come loose in the front end in the past 7 years (and how many miles?) but tires are always my first go-to part. Rotating is a lot cheaper (free if you do it yourself) than buying all new steering linkage and suspension components.
So try having the tires rotated front to rear to see if it changes. You could have some loose or worn out components up front too, but if the rig has low-mileage or the suspension and steering components are new enough, the tires are high up on the culprit list.
One good "curbing" going into a driveway, or one sideways glancing blow on a rock either on a high-speed dirt road run, or even a slow trail run with low air pressure could do enough internal damage to make even a new tire cause this.
If the tires are worn out mostly though, it's even more likely. Even if lower mileage, if the tires are 7 years old too, age alone could cause some issues. Mostly it's with the outer carcass, but sometimes a borderline defective inner belt can finally work itself out with time and mileage.
If the tread is worn funky, that's an almost guarantee of at least a shimmy. If other things are loose, it can get worse in a hurry.
So start there and let us know what happens.
Enquiring minds want to know...