Sure you can! I ran my best times @ 34, and started @ 22, never ran in high school or college. Nothing earth shattering (4:37 mile, 16:12 5K, 33:30 10K, 01: 13:33 Half), but I was only putting in mileage around 50, had time off in there for life and injuries.
My bread & butter was 16X200s with a 200 jog rest @ 1 mile pace (in season) for speed, 16-20X400 @ 2mile> 5K pace, 200 jog rest for endurance. Usually two workouts a week alt. with 8-10 X 1 min hill repeats hard for one or the other workouts depending if I felt I needed more speed focus or endurance.
Off season (winter) Fartlek once a week and keep the LR and pace in there every other. Needed the down time in the winter to recharge and refresh. I eased into the harder stuff in the Spring building pace and volume having mini peaks until Nov usually to hit goal races.
Long run was an easy 16, alt weeks with progression, fast finish type run.
You are smart upping the mileage, and you should get into the 15s fairly soon if you can keep the higher mileage up. I had just made a breakthrough but got injured and that was the end of my PRs. Just be patient, consistent, back off when you need to. Easier said than done, but it's just hard work and smart training you have to do. Good luck!