Thank you for the post. A key question would be, “How many more could you have done?” Did it kill you or, “Shucks, I easily had 4 left in the tank.”
You may already know this, but if not:
5:20 pace for a vVO2 type workout, with standing recovery - May net you about a 5:25 - 5:35 per mile 5K pace... unless the workout was very easy for you. That seems to line up with other posters putting you close to 17, just like your thoughts.
JD teaches that you want your HR closer to your training zone for the duration of the workout. Therefore, consider a 30 second walk, 2:20 SLOW jog, and 30 second walk in a workout like this.
We teach that you should do about 15 weeks of this workout at about 6400m total volume, once per week. If you are doing 6 x 1K, #s 5-6 should be a pretty good kick in the pants.... but you could do another if required. Cook the blood, but don’t burn it.
Cut it back significantly (About 4K in total volume) about 30-35 days before peak race. We do variations of this workout with less volume even in the off season. Bottom line, we spend a lot of time running at 3K pace throughout the year (the volume dictates the difficulty and potential for burnout).
At altitude, we run this as 800s or 600s with walk/jog recoveries.
Many coaching approaches teach that you should time trial to get a more accurate feel of your ability. Try a 3K at goal 5K pace. Try a 3.5 or 4K as a difficult workout a couple weeks out from your race. Dial in right on pace immediately and see when your world starts to cave in.
All the best -
RB