Looks to me like a lack of speed endurance.
I ran 17:02 on the road at age 46. At that point, I couldn't have matched your speed sessions, but I could run a 4:40 mile and 10:20 2 mile (indoors).
Your mile is only just inside 5:00, which is slow given how much speed you have in your faster sessions.
At 53 my times would have been very similar to yours, 1500m equivalent of around 5:00 mile and 17:32 5000m (track), but I couldn't have lived with your speed sessions. Last major session before the 5000m, I did 4x1 mile in high 5:30s, a little slower than yours but an extra rep. I could also do 16x400m with 200m jog at an average of 6 min per mile for the whole session.
So v my 46 and 53 year old selves (the time you want to run and the time you run now), you had way more short speed, but were 20 secs slower at a mile (the self you want to be) and equal at a mile and 5000m/5k at 53 (when you had way, way more speed).
I think the first problem is that your mile is slow for the amount of speed you have. You're obviously more fast twitch (as I was), so I think you need to get the speed endurance for a much faster mile (you just need the capability, you don't actually necessarily need to run one) and you'll have a much bigger cushion between your mile/5k pace.