Let's think this through just a little. It is basically August, 6 months from now will be February 1, not the best time to run your best 5,000. You need to think longer term. Think spring of 2018 or even spring of 2019.
I would start here:
http://www.runnersworld.com/race-training/solving-the-5k-puzzle
Don't believe everything you think you know about Runners World, Magill knows his stuff. That should get you to next spring and a few races.
If you get close to 16 flat, you are a year away and you are going to want to either find a training group, talk to your college coach or another coach in your area. You have most of a year to find them.
If you are more like 17 something next spring, you are really going to have to double down and it will likely take two years.
Good luck