You need to improve your endurance. Here, read this:
http://img.runningwarehouse.com/pdf/middle_distance_guide.pdf
It's long, but the main gist of it is contained in this quote: "This point needs to be reinforced to young athletes that if there is any “secret” to racing a fast 1500 or mile it is that it takes months of hard aerobic work that is just plain tough. To run a fast mile requires consistently hard 800’s, 1k’s and mile reps, 4-8 mile tempo runs and 12-18 mile runs at uncomfortable paces for the majority of the training year. The sustained “speed work” of fast 300’s and 400’s done in the spring is the fun stuff for the competitive miler. Performing the solidly paced aerobic sessions during the 8 months that precede this is invariably what separate the 1500m runners who make improvements in race times versus those who do not."
You need to be a distance runner for 8 months. Then at the end of the year once you have a huge base you get to be a miler. Don't worry about losing your speed, you can do maintenance stuff along the way, plus you race a lot in high school. It's easy to hop on the 4x400 regularly. That's enough to maintain or even improve your wheels.
I guarantee if you get that 5k under 16, your mile will immediately improve even without mile specific work. Your 800 will improve too, though obviously improvements there are small, 1-2 seconds.