What really helped me was having a set goal and small incremental increases to get there. Earlier this summer I worked up from <3 to >5 miles over the course of six weeks or so, at about your pace. Every week, I increased my mileage by 10%, and then dialed it back every third week for a recovery. That 10% increase was overall mileage for the week, and also the distance of my 'long run' which I would do once a week.
If at all possible, I'd aim for at least 3 runs a week: one short, one medium, and then your long run. So if you're running 6 miles/week now, run 1mile one day, 2 miles another, and 3 miles for your long run. Next week, run something like 1.3, 2, and 3.3 miles for your long run, for a 10% increase. You'll be up to 5 miles in a few weeks, and the increases are so small that mentally very easy to make it through.