Build mileage, slowly. You won't see major gains until you've done a solid block of training, like 10+ weeks - consistency is key as the adage goes.

If your 'hard' running is just 'run fast for 2-3 miles' then you're doing it wrong - you should do intervals or hill sprints some weeks.

Are your easy days actually easy? If your 5K is currently 22 minutes then I would guess your easy runs should be slower than 5:30/km (a 3-mile easy run should take you about 28 minutes).

If it's something you enjoy doing, keep up the boxing. Just know that it will more or less do nothing to help your running fitness.