Following with interest, I'm on a similar journey. When I was 18 to make our football team a sub 20 minute 3 mile was required. I have memories from uni when I was in competitive sport of smashing out 20 minutes on a treadmill at 16kph. Now I run at 11kphand 4k is a slog.
I've been steadily building back up to 5k and have been using intervals to help my progress. I currently run 4 times per week and one night of 11 a side football where I have already noticed a big improvement in my fitness. I expect I'll be around 26 minute 5k in about 6 weeks and then will see how I go from there. Depressingly I have a friend who started running about 4 years back and can now run 5k in sub 17 minutes.
The advice I have been give is:
1. Run frequently but be sure to have 1-2 rests per week.
2. If building for speed you will need to exceed the target distance by about 30%.
3. Work on your form and breathing patterns.
4. Lose weight
Yep, I also like the 80:20 strategy if it works.