Well, there's your problem.
No, 4-5K RPM won't wear it out. The PCM will bump up the line pressure. That's really not that much RPM, especially for a modern vehicle, but it's enough to keep the head(s) clean. My truck shifts quicker when I really get on the throttle. It softens shifts if I drive like a grandma.
My truck has seen countless 5500 RPM shifts. Original transmission. Only opened once to change the filter, and the pan was nice and clean, just a little clutch gunk on the magnet. Less than I have seen in many vehicles with fewer miles on the transmission. If I remember right, your car is on its second one, so I don't think keeping the RPM down did much to prolong its life.
I would get the engine up to temp before wailing on it, though I frequently hit 4K RPM pulling out of the lot at work, after the truck sits for hours. Again though, 4K isn't that much really. If all you do is short trip, it will probably benefit the car in many ways to get a good highway run in every now and then, once a week or so. With the car not getting up to temp and not seeing high RPM, it definitely has some carbon buildup. Take it out on your days off and run it hard on the highway. If you find that boring, get a different car. If you think it will kill the car, again, get a different car.