Hi Courtney,
Wow, a first 5k of 22 minutes, that's talent! I've been working my way towards something close to that, but its taken a lot of work and weightloss to acheive my recent PRs. As far as getting faster, you need to work on speed work for a 5k distance, but there is a lot to be said for doing long runs and tempos as well. I traditionally do 3 quality runs a week, a tempo run, speed run and a long run. For a tempo run, you would start with a warm-up, maybe 10 minutes, then run 2-4 miles (depending on your current ability on distance) at a steady pace that is challenging but maintainable for the duration of the distance, then finish it up with a 10 minute cool down. Speed work I would recommend doing some 400M/800M/1200M/1600M repeat workouts. As you build up your mileage you will be able to increase these, but my recommendation would be to do maybe 2-3 repeats for 1600s, 3-4 for 1200s, 4-5 for 800s and 5-6 400s. For each workout you will do a warm-up and cool down and in between the "sprints" you'll do a short recovery 2-4 min depending on what you need and then start the next repeat. The long run is a way to build your endurance at a slower pace, much slower than your 5k pace. It should be easy, no labored breathing, very in control. You should probably start somewhere around 2-3 miles and gradually build up to maybe a 5 mile run a week or two before your race.
These are of course my personal recommendations and are based on my own training plans. There are tons of plans out there for intermediate/advanced runners, so definitely do some research before jumping into one to make sure it fits with your goals, etc.
You should definitely continue with running and training, I think you have a lot of great potential with a first 5k like that. Good luck!!
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