Lots of 5 mile runs will give you the endurance you need to run a fast 5k. Going 10, 12, or 15 miles will not give you as much benefit as a solid 5 mile speed base will for a 5k. You want to set a half marathon PR? Break 2 hours for the first time? Great. Run 15 at least twice in the month before your race and you've given yourself a much better shot. Once you feel comfortable holding a given pace for 15 miles then holding a slightly faster pace for 13.1 on race day is in the bag. This also gives you a huge mental advantage.
Base and Endurance Conclusion
I didn't make a conscious decision to run lots of base miles in order to get fast, I did it to get thin. I got fast because I started with a solid base of slow miles. As I got thinner, it got easier to run faster, so I kept the same milage and just kept increasing the speed. Now it feels really awkward to run any slower than an 8:00 pace, and when running outside with no Garmin telling me to slow down my natural gate keeps about a 7:30 pace. I know how to push that up for shorter distance races and can force myself to slow down for longer races.
So build your base, then add some endurance and your speed will follow. Give it 6-15 weeks to really get a solid base established. I took 5 months leading up to my ironman training plan to really get that base established and only ran more than 6 miles three or four times. Consistency is the key. Unlock your potential!
Next up is going to be how to get fast at swimming and cycling!