Standard races are 5k, 10k, 13.1 miles [half-marathon] and the marathon 26.2 miles.
College level cross-country races are 8k or 10k.
Set up your own 5 mile course. Goal: finish it. You can record your time, but speed shouldn't be your goal. Not yet. [Chris is right - 5 mi in 30 min is WAY harder than running 1 mi in 6 min.]
If you keep "5 mi fast as possible" as a goal, your training will change. Alternate intense days and easier days. Right now, your intense day could be running two miles at a hard pace, and a rest day might be swimming, biking or jogging for 20-30 minutes.
Intervals are an option for intense days. 400m or 440 yd intervals are a good medium distance. They require both speed and endurance. 50m or 100m require speed.
There are lots of ways to make running interesting.
One way is to run a course that will give you an obstacle about every minute or so - something to jump, climb, balance, quad movement, lift, carry, throw, etc. - and try to go non-stop for 20-30 minutes. It's WAY harder than only running. If you can't keep running, slow to a walk until you catch your breath, and then speed up again. Don't stop.
Experiment. Have fun.