Stick this thread out for a while. You’ll likely learn a lot. Unfortunately, I am not the expert on physiology, but I think I can get you in the right directions and bridge the gap between science and laymen terms.
(My apologies if I present anything you already know. It just easier to start at the bottom and work up).
Your “aerobic” zone is typically what a lot of us will refer to as zone 1 and/or zone 2. This takes you from 65% of you max hr all the way up to ~80% of your max hr. Ideally if you are well trained, you should be able to stay in these zones for a really long time (several hours). This could be power walking, jogging, and coversational paced running.
Zone 3 has been called the marathon pace zone, the blue zone, the moderately hard zone, or the fast running zone. This is where the breathing gets somewhat labored. This typically is from 80-88% of your max hr. A well trained runner should be able to race 15-30 miles in this zone (2 - 3 hours).
Zone 4 is erroneously called LT. Its actually the zone where you maximize the training of you lactate threshold, but is significantly faster than lactate threshold. The proper term is maximum lactate steady state (MLSS). This is at around 88-92% of your max hr. You should be able to race at this pace for an hour (if trained). That is typically somewhere between a 10K and a 20K race.
Zone 5 is your Vo2max. This is getting very close to your maximum heart rate. (98+%) This is where your body takes in as much oxygen as possible to use for exercise. At this point you should be able to race for 10-11 minutes (Andrew Coggan disputes this, but this is the info that Jack Daniles has provided. AC seems to think it should be for less time). This will be for about a 1.5-2 mile race for most triathletes.
Zone 6 is faster than V02max. Typically this will be races that last only a couple of minutes.
Sprinting - THIS is anaerobic. You can go completely anaerobic for ~10 seconds (maybe up to 20…not sure).
So, the main point here is that there is a lot that happens between zone 2 and sprinting that is not considered “anaerobic.”
Regarding your 5K race, I’d expect you to be able to maintain ~95% of your max heart rate for a 20 minute race. I’m guessing that would be in the high 180s for you if they are actually using 80%max hr for the top end of your “aerobic” zone.
Anyway, I hope that helps. I often screw up a detail here and there, so look for people to offer corrections.