I'd second the previous advice to add some tempo.
Being in sub4 shape typicallly means your 5k should/would hover around the 14 min. mark. Your 14:35 effort shows you're a tad deficient on solid lactate threshold work. In my opinion, this is a huge aspect of miling correctly.
I'd add some 6-10k tempo runs at what you'd figure you could run a 15k in right now; if you can't handle a full 6k to start, break in up into 2 times 3-4k intervals with 1-2 min. rest between; then continue to build on that until you can handle a 10k. I'd do these type of sessions once every two weeks to start (as they can be taxing if you're not used to doing them). Maybe next season, with more background, you could move to once a week during your base phase.
These types of workouts more than likely will produce much faster 800 times as well. Good luck.