It is an ambitious goal, but not overly ambitious. Goals are supposed to be ambitious. So I would shoot for 14.15 but definitely don't beat yourself up if you only run 14.30-14:40, you should be happy with that too. If you are running 14.45-15.00 then, I would be self-critical.
I ran 9:15 in 12th grade. Then I ran 8:26 3000m as a College Frosh (which converts to like 9.05-9.10 I believe). As a College Soph I ran 14:11 for 5,000m. So based on my progression, 14.15 should be in the realm of possibility for you.
For me, the training/life style that I attribute to attaining that time is very consistent doubles. The winter before I ran 14:11 in the spring, I woke up at 6:00 am every day M-F and ran in the morning and then went to class. As a frosh, I did a few doubles but not with the same consistency that I did as a Soph which was every M-F, 6:00 am, 4-5 miles, I literally did not miss a day. That takes a certain lifestyle. If you stay up late, drink, etc., you are gonna miss a day (either oversleeping or injuring yourself due to lack of recovery). With doubles like that 80+ miles per week was consistent. With several months of base like that, I had the endurance to maintain prior 2 mile pace for 3 miles.
More important than anything, I would say, is not to quit or give up. Eventually, I leveled off my improvement and quit running. Gained a buncha weight, and now I would give almost anything to just be able to run a 18 min 5k.