4:45 for a sophomore is promising, and it shows only a slight drop off from your 800 time (4:41-42 is more of an equal performance.) That kind of thing will come about naturally with consistent training.
Some things to keep in mind for a 16:00 5K.
That's about 5:07 per 1600. That's probably a hair better than you can hold for a 3200 right now, so you're talking about adding another 1800 meters at that same pace.
You'll definitely want to run a little at that pace about a month before the season starts. 1000m and 1200m repeats at that pace (3:24 and 5:07) will get you ready for whatever workouts your coach will give you during the season.
Getting to that point is going take a little increase in your mileage. You definitely want to shoot for a long run of at least 60 minutes once a week, but I would cap that out at around 75 minutes or so. Also, your best friend early on will be your tempo work. Tempo pace for a 16 minute 5K runner is about 5:36. Of course, if your goal is to run 16:00, then you'll probably open the season closer to 17:00. Since that's the case, your tempo work should be more around 5:54 per mile. Ideally, you'd work up to running 20 minutes at this pace and have it feel hard, yet not like a race effort. You will most likely not be able to handle this run properly at the beginning of your summer, so I would recommend running 3 miles worth of tempo pace in repeats with a 1-minute rest (i.e. 5 x 1000 at 3:41 or 3 x 1600 in 5:54).
A lot of people might tell you to not do workouts during your base training. But there is a big difference between working out for races and using interval workouts and tempos to get you ready for a competitive season. From early September to mid-November is really only about 13 weeks, that's not enough time for a coach to take you from your base phase to peaking for championships.
Good luck with everything. The best advice I can give you is , once the season starts, put your faith in your coach. You've obviously got a pretty good one because your times are legit, and as long as they are not a complete idiot I gotta believe you'll run faster than 16:30 this season. You just need to come into the season ready to do work.