OP - this is a reasonable assessment imho. Spot on.
With that in mind, assuming you *are not* built like a fullback, someone can potentially start where you are, and run 4:20 or faster in 12th grade. This will involve improving both speed and aerobic fitness over the next 3 years, and in my opinion there are no better 3 years to make the biggest jumps that the 3 years you have upcoming :)
You will need a plan to develop speed. And you will need a plan to develop aerobic fitness. This is a long term thing, that will take time and dedication - if you want it, the journey is yours.
Aerobic fitness in the off season can be developed in 2 basic ways: easy runs and tempo/threshold running. For a developing young athlete, I'd suggest something like:
Mon/Tue/Thu/Fri easy runs both AM and PM. Start with just 20 min (or whatever makes sense) each and build up to as much as 45 minutes, but keep it easy and doable. More isn't better unless your body is ready for it to be EASY.
Wed: Alternate 20 min tempo run one week, with 6 x 800m another week. Jog 400m between the 800m repeats. Look up your proper threshold repeat pace on an online calculator, based on your 5:20 PR. And next summer, replace this with 5 x 1000m with 200m jog. The following summer, replace this with 8 x 1000m with 200m jog.
This leaves Sat/Sun. For now, I'd suggest speed development on Saturday and RECOVERY on Sunday. Remember, recovery is part of training, especially for speed.
Sat summer speed session - I'd suggest 5 x 80m hill accelerations, 5 min full rest. Do a full gentle warmup to prepare. Accelerate smooth and the last 40m should be FAST. After rest, do 3 sets of bodyweight squat-jumps. Start with maybe 5 and increase up to 20. Then, 3 sets of lunges (forward, side, diagonal), start with 5 ea and build up to 50. Then, 3 sets of heel drop/ calf raise single-leg bodyweight, start with 5 and build up to 20.
Also - a set of drills and strides after the Wed session is a good idea.
Just an example, hope this helps :)