I would have a coach look at your running form. Your 800 time is only two seconds slower than your 200 meter time times 4. Maybe there is something that can be corrected that will make you faster. Just a thought.

Your instincts and analysis are accurate. To run faster you have to run faster. Your 32 sec. 200m speed is a limiting factor to racing faster middle distances.
The 200m speed with respect to the 800m speed is interesting. The 200m pace for a 2:10 is 32.5, so you are near max speed for 800. With that kind of muscle stamina you should be able to go under 4:40 for the mile.
The above posting referring to form may be the ticket to your speed improvement. Pure speed is a function of running mechanics. Improvements in foot-speed, stride mechanics, upperbody involvement, and muscle strength can be made that will improve pure speed. During the preseason to track we work hard on form drills to enhance speed. Improvement is tracked by timing 40 yard sprints. The goal is to get faster, so we use the 40 as a measurement of pure speed. Once a week we will time 3 - 40's and hopefully each week is a slight improvement.
There are videos available that could be helpful. Check with Track and Field News.
Try running a few 50-150s after your daily continuous run workout and play with your speed. Sprinting is a different mental attitude than distance running. Its very aggressive.
A classic Lydiard workout is a mile's worth of 50s; sprint a 50 then jog a 50 repeatedly until a mile is covered. Thats a workout if done with intensity that can get your blood up.
Good luck.

I hate to say it......

but, hitting the weights doesn't equal a sub 16 5K. Weights may improve your 400M time but its going to kill your 5K time on a track. You want to be light and efficient.

If your primary goal is break 16.......you have to improve your mile times......your 4:50 pr is only 10 seconds off the pace that you want to be running for 3.1 miles. you got to hit the 800 and 1000 meter repeats hard. if you can run smooth and steady 1000meters (w/small rest periods), you will be well on your way.

mileage should be your first focus.....

good luck.

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Brian

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Just wanted to chime in here a bit with my own personal experience.

In the summer after my first year in college, I decided to try a 400 all out on my own. I ran 59.6. This was in May. I was just coming off a season and felt like giving it a shot. As I began to build my base up, I incorporated hard accelerations (10 X about 70-75 meters, the distance between two light poles on my street) 2-3 times per week and I also would throw in some 150's at increasing efforts. It would look something like this 4x150, jog a 50 for recovery, 150's at 2 mile pace, mile pace, 800 pace, 400 pace. If I was feeling frisky or had a short run that day, I might do 2 sets of that. None of these speed sessions were terribly hard and my emphasis was on building my distance base for the upcoming season. At the end of may, I ran a 400 with a friend of mine and hit 56 seconds. In july, after the 2 mile at an all comers meet, I was talked into leading off a 4x400, Which I did in 54.5.

During this time, I raced a few times at 800 and lowered my PR from 2:10 to 2:04. I never did any "hard" runs, although most of my mileage was in the hills in some way or another. The cross country season I was 5th man on a team that won the Nor-Cal JC championships, then in track I dropped my 5000 PR by 30 seconds and my steeple PR by 17 seconds and my 1500 PR by 8 seconds and ended up 2nd in my conference for the barrier race.

I think that being able to run faster all out had a big part in my improvement in that I was able to run more comfortably at speed.