Sounds like your doing great. The key when you up your distance is to do it slowly. build no more than 10% a week on your distance. Make sure you do plenty of stretching particularly AFTER you run. For core work I just do various situps and pushups. At 42 your not that old to start. I'm 52 and started at 47. The key to keeping it going is getting into a dedicated routine.
There is a lot of useful Web info on weight training and core strengthening exercises, but I would also recommend investing in a session with a personal trainer who can provide you with a customized program tailored for runners. I did that about a year ago and found it very helpful. I did one session with a trainer affiliated with my gym and received an excellent set of exercises tailored both to complement running and to my body's individual strengths and weaknesses.
@ 5K: Angels Baseball Foundation 5K, Anaheim, CA, 24:15
Friends of the Villa Park Library 5K, Villa Park, CA, 24:10
Claremont Sunrise Rotary Turkey Trot, Claremont, CA, 24:23
@ 10K: Great Race of Agoura - Old Agoura 10K, Agoura Hills, CA, 50:31