If you're hitting wrong notes after resting, you are probably hitting wrong notes when you are practicing tired as well, while being less aware of them. If your fingers get sore and tired after two hours of practice every day for several days, then you are likely trying to force a technical goal to happen with extra effort, rather than becoming aware of the most technically economical way to realize the musical task at hand.
I would first advise you to pay closer attention to the music, even the music in five-finger exercises. If there is a wrong note, even to the point of hitting a note louder or softer, or sooner or later, than you intend (and do you know exactly what you intend? Where the mind leads, the body follows), go back and correct it. As I'm sure you have heard many times before, you will develop a great deal more speed by slow practice with the goal of making everything exactly as you intend than by putting out maximum physical effort towards the goal of playing fast. The fact that you say that your practice sessions are "intense playing - trying to develop speed and accuracy" suggests that you have relegated the primary goal of playing music to a secondary one behind playing with speed and accuracy.
What is "accurate" playing? I believe you will profit from thinking more about this. How much time and thought do you give to musical considerations rather than technical? The technique follows the musical purpose, and the biggest mistake we pianists make (and we all do to one degree or another) is to believe that we will first develop the technique and then put the music into it. That is very much putting the cart before the horse. So first, reevaluate your priorities.
Now, some purely technical considerations to think about. (Which again, you must think about only in the context of how to realize musical ideas--I can't repeat this often enough!) An important principle is to get all your muscles out of one another's way. If you start feeling strain, it's because you are making unintended isometric muscle movements (one muscle working against another, as when you push both palms together as hard as you can). This happens more as the muscles become tired, but to some extent it always happens.
Part of technical improvement is to continue to eliminate isometric exertion at finer and finer levels. Part of it is to strengthen weaker muscles, of course, but this should always be done in the context of getting muscles out of one another's way.
Another consideration is to work to position yourself (whole body, from fingertips to feet) in such a way as to realize technical goals with the least effort. It's particularly important to be aware of the limitations of tendons and ligaments, and work to keep everything in the most natural alignment. I will say that I rarely got any sort of repetitive motion injury from playing piano, but I did when I first took up computer programming for a living. I applied principles that I had learned from studying piano and found that they went away.
So again, where the mind leads, the body follows. Find the music, imagine how it will sound, let that sound come out on the piano. Conflicts in the mind become conflicts in the fingers. Clarity in the mind becomes clarity in the fingers. Keep working on it, and when you are old you will have something that is worth working on still.