My teammates and I had a good group of guys who were either 800 or 1500 guys with slightly different unique strengths.
1) 49.9r, 1:52.7, 4:08 (never seriously attempted, but likely in ~4:00 and 15:50 shape).
2) 1:52.9, 3:48, 14:50
3) 1:53.1, 3:52, 15:4X
4) 50.4r, 1:53.7, 3:58, 15:4X
I was runner #1 in the above example, and while I was in PR 5k shape, I obviously wasn’t optimally trained for it as my focus was on the 800. But many of the above Runner’s, especially the 14:50 guy, had a really good base built up before track season. I had been doing more sprint work and lifting where as the 14:50 guy had come off a year or half Ironman training, but was formerly a 50.x 400m runner in high school. But all of us had a good base.
During season runners 2 and 3 did a lot of mile pace work. Most of it goal mile pace work in the form of 600s, 400s, and 300s. That mixed with some 800m pace work mixed in (I.e 3x400m a little faster than 800m pace) and tempos and progression runs.
Runner 1 and 4 did more 800m pace work. Typically once a week we’d do 200s and or 300s at goal 800m pace. Towards the end of the year we would add in 400m pace reps and 400m reps at goal 800m pace or faster. Other workouts that were sprinkled in to supplement were tempos/cruise intervals, progression runs, 3k-5k pace reps and occasionally mile pace reps.
It’s impossible to be 100% optimally trained for all the distances mentioned. But you can get into very good shape for all. I’d train more like a 1500m guy and make sure you are occasionally running around 400m pace, even if it’s just a weekly set of strides. Same with tempos. You won’t need them during season every week, but never get too far away from touching on that end with your desire to run a good 5k.