Does the Gen III have adjustable rear suspension? Do bad things really happen if the wheels are not rotated front to rear every 5000 miles?
I am not sure what you are asking in your first question. Are you asking if the Gen III has adjustable rear alignment? If so, the answer is no that you have to use shims to adjust the rear alignment. Bad things do not happen if you do not rotate your tires every 5000 miles. The only thing that should happen, assuming that you do not have an alignment problem or uneven tire wear pattern, is that the front tires will wear faster than the rear tires. There are several threads on here about the pros and cons of rotating tires. I personally prefer to rotate my tires every 5k miles for even tire wear and then change all four tires at one time one needed.
The Toyota shop manual, most dealers and the average alignment shop will tell you the rear alignment isn't adjustable. It can be adjusted with aftermarket shims. The front toe and camber are adjustable but adjusting front camber requires some different bolts. Toyota stocks those bolts. The front tires will wear out much faster than the rear tires, but nothing really bad will happen unless you have alignment problems. If you don't rotate your tires, you will be replacing your tires 2 at a time. You might end up with different types of tires on the two ends of your car because companies don't make the same model tire forever. That's not good because cars generally handle better with a matched set of tires. The tires that are rear only might last long enough that age starts to become an issue. A good compromise would be to rotate your tires at 10k mile intervals.
if you don't rotate, your tires might wear prematurely. i say MIGHT. because they wear in the same places if you don't rotate, you may not get all the usefullness out of the tires replacing them 2 at a time. i learned this the hard way.
If you rotate your tires at 5k miles, when you reach 10k I don't think you have to rotate again since now each tire will have been on the front for 5k miles and on the back for 5k miles. Next rotation would be at 15k miles and then again at 25k miles. Does this theory make sense ?
I've followed Toyota's recommended 5K rotations on both my Gen ll's, and had excellent service out of the OEM Integritys. Over 63K miles on the first one, and now nearing 60K with my '06 with plenty of treadlife remaining. I've done a lot of the rotating myself. If I keep the next one long enough to replace the tires, I think I'll go with Costco for the free rotations. (Lots of the retail tire chainstores offer the same thing.)
The tires may also have uneven wear if tire rotation is not done on a regular basis. Front tires have a different wear pattern than rear tires due to cornering.