
Recovery, as the smart people say, is underrated.

Recovery, as the smart people say, is underrated.First let me give you the good news. Consistent, steady-state running works as well as speed work to improve your speed, at least at the start, and for runners at our age. Now, I'll ask a rhetorical question: Why do you think you need speed work? If you are looking for a change in your training, you probably don't need as much speed work as you suspect. However, it's a nice change of pace (no pun intended) from doing the same route at the same pace day after day.
If you're looking for a change of training focus, then you can do a number of good speed workouts without depending on a track. All these assume an out/back route, but you can adapt for a loop course:
Progressive Tempo Run - run at an easy pace for the first half (time), then slowly increase the pace for the same period of time for the second half.
Intervals - run easy for the first half, then pick up the pace for 30sec to 1min, with equal-to-twice the time back at the easy pace for recovery; if you pick up for 30 seconds, then run easy for a minute, pick up for a minute, run easy for two... This is kind of like fartlek (speed play) workouts, but a little more structured.
Your jumps in performance are probably due to the patient manner by which you have progressed so far. You won’t be hurt by continuing what you're doing for two to three more weeks before trying a 5K. Once you've done that you might think about either another three-to-four weeks of steady runs, or adding in one speed workout a week; do the progressive tempo one week, do the fartlek-type the next. If you plan to focus on speed for a specific distance, I would use both of those workouts two times a week, or split it up with a weekly tempo run (75% effort for 20-30 minutes). Add one long day (no more than 1/5th of your total mileage for the week) and easy runs during the other two or three days during the week. Oh, and one rest day a week is a must!
Make certain your form is good throughout your workouts; erect posture, “plumb line” from the top of head to the shoulders, spine, and hips; relaxed shoulders and hands, with your elbows bent at no less than a 90-degree angle. You should propel yourself across the running surface as smoothly as possible, with no “bounce” of the horizon, and as quiet a foot strike as possible. If you place an earplug in one ear you can listen to how hard you are pounding on the running surface. When talking about distance running, quieter is always better and more efficient.
After three-or-four weeks of that, then consider another 5K as a test to see how you're doing. After a second 5K test you might want to add an additional speed workout during the week. Let your conscience be your guide. As my coach has told me in the past, running is a sport of PACE and PAtienCE.
If I lived in Chicago, or worked at Great Lakes it would be necessary to have good stuff. Yes, that leather bomber jacket was barely functional without a sweater/vest underneath. Seriously microwaved cup of coffee makes a good handwarmer...for a time.
We were leaving our workout as a friend, an ex-university cross-country coach/national-class marathoner was coming in to get his workout. How shocking to hear he hadn't run more than a dozen miles a week since the beginning of the year, but his focus has been on academics. I bet his 12 quality miles were more effective than my 40-50 junk miles...junk being a relative term.
WHAT ARE YOU READING NOW? Will/Ariel Durant's History of the World, Volume 10(?): Rousseau and Revolution. Also reading David Maraniss' Rome 1960: The Olympics Which Changed Everything.