CrossFit has helped me go from running a 32 minute 5K to a 23 minute 5K without a lot of run training. HIIT works if you want to go a less running-heavy route.
There are a lot of ways to run decent times without doing a lot of running. It doesn't surprise me that you 5K time improved dramatically with the type of training you were doing. The important key is for someone to do the type of training they enjoy. I've always lifted weights in addition to running and did my best running when I added rowing on a Concept2 erg twice a week.
When my grandson started running as a freshman, it was obvious he had to mature and get a lot stronger. My daughter and her husband spent a lot of time with him developing his core strength (read "grandfather brag" for the results of this type of training) with some pretty good results.
