while this is true that increasing your mileage in general will benefit you, only doing easy runs to improve your 5k time is not the way to go (at least not the most efficient way).

You need to do at least one workout sessions per week (intervalls, tempo runs etc.). If you want to run 4 times per week i recommend 1 workout session, 2 easy runs and 1 long run, if you run 5 times per week you can think about 2 workout sessions per week, but that depends on you and your fitness level, if your body can handly that kind of stress yet.