I also think you would benefit in running the occasional 2 mile time trial. If your goal race is 5k and you are never racing shorter distance, if you are going to PR at 5k, you're going to be going through 2 miles faster than you've ever run in your life.
If you were a track runner, you'd generally race 1500m and 3000m as well as 5k/5000m and you would have had the experience of going through 3000m at a faster time than you'd be running for your 5k best.
You're going to feel a lot more relaxed in the early stages if you are running a pace slower than you've run for 2 miles.
Since you are running for time, rather than being in a true race situation, you are going to get the biggest bang for your buck with aerobic development. You can do that with tempo runs just a bit slower than you're LT pace (rough guide, the kind of pace you could run for an hour), or you can do it with interval sessions at a similar pace (say 6x1000m with 800m slow jog recovery).
To answer the original question, if you want to get sub 18:00 you could get there on a diet of tempo runs at 6:15 per miles, strides, and the occasional 3000m or 2 mile time trial.