I have a similar story to others who've already posted. It basically involves the "been there, tried that" frame of mind.
Lesson #1: I had a season where I ran everything at a hard pace. I ended up injured, and am still dealing with it today. Not worth trying. Injuries make you useless.
Lesson #2: I had a 'season' where I ran everything at an easy pace. For 7 months I ran an extra 40mpw greater than I had been for the previous year, only to improve my 5k time by 25 seconds. Not worth it. You need to stay in touch with your speed.
Lesson #3: The times that I dropped large chunks off of my 5k pr was when I jockied between long (or long-ish) easy stuff one day & some harder stuff the next day, back & forth.
Lesson #4: I began to mitigate my injuries by recently adding some lifting. I lift 3x per week, and never on consecutive days. I go out of my way to work my hamstrings (on a machine where you lay down on your stomach), and various things I'm trying to work on glutes. Jury is still out on all of this for me.
Answer to your question: You should NOT listen to your coach because too many consecutive hard days will ultimately hurt more than help. Your current total mileage is too low. You need more easy running at whatever pace is 60 to 70 % of your max. heart rate, but every other day do something at a faster pace (whether it's 10k pace, 5k pace, mile pace, 400's, or 200's, just make sure you vary it).