I did it! I am amazed with myself, but I finished it this morning. There are still times when I don't feel like going out running, but I recently read that, with exercise, you'll never regret it if you don't go and do it, but you will frequently regret it if you give in to laziness and stay on the couch. If I can do it, anyone can!
That said, although I can run for 30 minutes non-stop (32 actually, because I've made my own playlist), I'm still not running the full 5k distance. But in way that's good because I still have something to aim for. I'm determined to carry on and get to the 5k mark. But at the moment running for the full 30 minutes is good enough for me.