Agree with the hill reps & agree with a lot of this (maybe minus 4xmile- that's the hardest 5k workout out there, no way to progress it & 3x is probably fine).
The best way to run sub-15:00 pace is to run sub-15:00 pace. When is the last time you did a 12-16 week dedicated 5k block? 1 VO2 max workout/week @ sub-15:00 pace. Cycle through stuff like: 12-16 x 400, 10 x 600, 6-7 x 800, 5-6 x 1k, 4-5 x 1200, 3 x 1600. Do some over/under distance stuff too -- faster 150s-300s, & reps up to 600 @ 3k pace, and tempo/threshold stuff. 4 workouts every 2 weeks -- 2 VO2, 1 under distance, 1 over, ez & shorter than you're used to long run, ez & shorter than you're used to daily runs.
What you can do in a 12-16 week block is to hit those VO2 workouts early in the build with decent rest and then repeat on less rest as you get closer to a race. Race selection matters for you. Find a college meet that will allow you to run unattached and has a 5k with some depth at that time. Think about time of year/weather. Find something in the spring so it's not too hot. Try to find a place that isn't usually too windy. Then let it rip.