It is true that time slows down for someone who is moving at almost the speed of light, and slows down more as they move closer to the speed of light. However, time does not slow down for people who are standing still, it is just the same as always. So if one person stood still for five minutes while another one ran around him at a speed near to that of light (which is 660 million miles per hour), the person who stood still would only age five minutes. The only surprising thing that would happen would be that the person who was doing the running would age somewhat less than five minutes. For example, if the person ran 600 million miles per hour (i.e., nine tenths the speed of light), they would only age about 2 minutes. If the person ran 1 million miles per hour (still much faster than any rocketship or bullet), they would age about 1/1000th of a second less than five minutes. So for speeds which we normally encounter on Earth, this effect of time slowing down is almost always immeasurably small.

I don't know if the numbers you are giving are correct, but the idea is.
The person moving at light speed does not cause the person in the middle to age, though.Both people experience their own relative sense of time. The moving person would sense only five minutes and the still person would actually experience 50 years. The only time when their experiences would be comparable is when either the moving person stops moving or the still person begins to move at the speed of light. What happens is that one person enters the frame of reference of the other! Neither person affects the other's sense of time; the still person does not cause time for the moving person to slow down and the moving person does not cause time to speed up for the other person.

The answer to the question of why is a little harder. Remember that speed, like miles per hour, is just distance divided by time. Also remember that the speed of light is a constant, it does not change. This means that I could never race a laser beam or I could never move so fast that I could actually see the tip of a laser as it moves across a room at the speed of light. This is because the beam would have to move at about the same speed as I was moving--the speed of light. But to me, the tip of the laser is moving along side of me and has a relative speed of zero. This is not possible because the laser has to move at the speed of light relative to anybody, moving at any speed. It has to move at the speed of light. So no matter how fast I go, the laser is always moving 300000000meters/seconds faster! How is this possible? Well, if distances cannot be made shorter, then time must be slowing down. So for light to move at the speed of light even though I am moving at the speed of light, time must have slowed down for me so that the laser moves faster. Kind of like when you are having a dream where everything is moving in slow motion.

This seems to be a variation of what is called the "twin paradox." Imagine you have a set of twins. One gets on a spacecraft and travels for a while at almost the speed of light. The other twin stays on Earth. A consquence of Albert Einstein's special relativity is that clocks seems to move slowly to someone who is moving very fast compared to the person standing still. This amazing idea has actually been shown to be true! Anyway, if the twin on the spaceship comes back after he thinks it's been a year, the twin that stayed on Earth may have aged 20 years or more. But you might argue that from the spacecraft twin's point of view it was the spacecraft that stood still and the Earth that was moving away very fast. So how come it was the twin on Earth who aged?
The answer is that in order to get the spaceship moving at close to the speed of light it had to accelerate a lot. It turns out that the predictions of special relativity are not valid for a person who is accelerating. So there is no paradox after all.