First of all, I can give you first hand experience on this because I ran cross country through all of high school, so don't just disregard my advice
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5k (3.1 miles) is not much at all. In fact, that might be too low. At 16, I would run up to 8/9 miles a day, although I wouldn't do this every day since this isn't exactly the healthiest thing. Some argue that you can run heavy distances without injuring yourself as long as you have proper form. I think this is a pretty stupid comment since they suggest that you can do 150 miles a week without suffering injuries. I don't think I ever did more than 80-90 miles in a week, and that would be at the peak of my workout time. Generally, I would mix in interval workouts once a week during the offseason (they are more speed-based instead of distance based); each week, you do more distance (such as going from 4 400 meter runs to 6 400 meter runs) with the same amount of rest between each 400. After you build it high enough (10-12 400s), you start again at your starting number and do it with less break between each set.
Proper form can be attained from running barefoot. Yes, that's right; running barefoot. Your foot was designed to make direct contact with the ground. With shoes on, your feet don't make contact with the ground. Because of this, people often 'crash the ground' when they run, which makes them more succeptible to injures (stress fractures are common, I had 2 at the same time. From then on, I trained barefoot and I haven't had any injuries ever since). When you run barefoot, you run more lightly instinctively, which helps you out. You can't run barefoot just anywhere nowadays; a clean field is a good idea. Even a track with a soft surface can be used, although I prefer to run barefoot on the dirt and grass instead. Avoid concrete, although run with shoes on if you run on concrete (to avoid glass, rocks, etc). Nike released a pair of shoes that they claim makes you feel as if you're training barefoot; good idea, but it doesn't beat running barefoot. Give it a try if you want.
Seriously, don't worry about breathing. Just breathe in through your mouth and out through your mouth. A small number of people suggest breathing in and out only through your nose since this keeps a balance of CO2 and O2 in your body and all this scientific stuff about aerobic vs anaerobic respiration. I think it's stupid to breathe only through your nose...I've tried it and I just couldn't get enough oxygen. I can do it when I'm running on just a flat surface for a little while, but once you hit the hills, it's damn near impossible to breathe just through your nose. You generally tend to breathe in rhythym with your steps sort of, but honestly, I don't think you should get technical about it.
I hope that helps somewhat. BTW, are you just training on your own or are you training for a cross country team or something?