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: Ontario Mills 5K, Ontario, CA, 25:17
New Balance Palm Springs 5K, Palm Springs, CA, 24:32
@ 10K: LA Chinatown Firecracker 10K, Los Angeles, CA, 52:15