Totally agree with the focus on speed & power. It takes time, but there are no shortcuts. And people who complain "I'm old & can't do it anymore!"...I'd ask, how often do you train it? The answer is telling. Ways I do it:
1) On workout days, 6x flying 30s at max speed before my workout as the 2nd to last thing I do in my warmup. These are not gonna ruin your workout, it's just 2-3s of max power output. No fatigue. Purely training the nervous system.
2) Last part of my warmup: 1-2x flying 100m at 95%. I've worked this down to 12.0-12.5 range since I started running competitively again in my late 30s & a 15.0 felt like an all-out sprint lol.
3) Daniel's R pace stuff. Full recovery to focus on GREAT FORM and efficiency. 200s at 31-33. 400s at 64-67. I'll start a multi-pace workout with some of these, then get in a 2-3 miles at Threshold (which feels like cake after the Rep pace work)
4) 6-10x 800-1600 pace strides between 20-35s on 2 recovery days per week. Make one day up not-to-steep hill.
5) Do other athletic stuff, like jump! 2x a week as part of my warm-up, I jump. 1st grabbed a basketball rim at age 14, can still do it at 40 because I still train it.
That said, as the brojos say, "strength is speed", so you gotta do stuff like above AND the longer work - I do 4-5mi at 5:20 pace as part of my other main weekly workout. Gotta work both ends!
Personally, I respond & do very poorly at 5k pace workouts with substantial volume in training (e.g 5x1k). They leave me knocked-out & unable to do more "volume of quality" in the week. So I only use them as a "predictor-style" workout that tells me where I'm at (not to get me to my destination).
And to the poster saying you need 75mpw+ for sub16....I disagree. If you have two "hard" days per week (two workout days) & one "medium effort" day (a long-ish run)...everything else needs to be short/easy (with those strides mixed in), or off. Recovery becomes WAY more important that miles at 40yo and up. I take a day off per week, and barely hit 40-50mpw.