Kinda disappointed in these responses so far, do better LRC.
You can absolutely make that improvement. I am unsure if it is the most likely outcome, but that type of improvement is not at all unheard of. Train smart and load up on easy miles, LT, and tempo, most importantly stay healthy and don't burn out, and you'll be good. Going from running 2 miles at 4:57 to 3.11 at 5:02ish is an improvement to be sure, but nothing nuts. I didn't do anything special my junior to senior year summer and I made a pretty similar if not slightly larger leap. If you're an endurance type, you might be able to get close to breaking 16 right now with only a little bit of 5k-specific training, so 15:45 is not at all absurd.