some people here are suggesting just doing easy runs instead of interval work because the OP is inexperienced and is running a 22min 5k.
Though I agree with that rational to some extent...if OP enjoys doing harder runs and only chooses to run 3 days per week, then he/she will get faster in any case. Doing intervals might satisfy the need to feel like one is improving every week or month, where running at 9 or 10min pace all the time may not inspire confidence and further motivation.
My recommendation for a 3 day per week training plan would mimic many of the others suggested here.
1. interval workout, either flat or uphill, with a volume around 3-4 miles of hard running. this could be 12x400, 4x1mi, 6x800, etc. just mix it up, and aim for recovery periods of about 1-2min for repeats of 400m to 800m, and 2-3min for repeats of 1000m-1mi. try not to run more than 10sec/mi faster than 5k pace. if that's too easy...do more repeats.
2. moderate run, or tempo. 30 minutes should be good at a pace about 30 to 45 seconds slower than current 5k pace.
3. "easy" longer run of 8-12mi, increasing in pace and/or distance every couple weeks. should be hard but sustainable.
the effort level for all 3 of these runs should be moderately hard, but never a :gasping for air" or "hands-on-knees" type of effort. uncomfortable but manageable.
and obviously, keep in mind that it's much easier to improve if you run more than 3 days per week, no matter what kinds of workouts you're doing. if you wanted to add to what I suggested, just add more jogging in the warmup or cooldown, or add a 4th run.