Well, you're certainly young enough; if you put in the effort you *might* actually get down to a 10 minute 3K.
Based upon your recent post, are you saying you're working a program to get you to a 50 minute 10K, or are you saying you can already run a 50 minute 10K?
If you are already running a 10K at roughly an 8:00 per mile pace, then you will probably need a good year and at least 2,000 miles of fairly intensive training to get down to a 10 minute 3K; if you've not yet achieved the 8:00 pace, then it may take you more like 18 months and 3,000 miles to get you to your goal, and even then it may prove elusive.
The thing is, running a 3K at a 5:20 pace requires a fairly stout biomechanical infrastructure to avoid injury, and said infrastructure cannot be built overnight without causing injury in the process. Keep in mind that your muscular and cardio-vascular systems develop at a faster pace than do your bones, tendons, ligaments, and joints, and those latter systems require months or years to develop.