Hah! What's a "normal person"? If you are regularly training at an 8:30 pace, say 15 miles per week (mpw), you can probably beat that pace in a 5K race. You may very well be capable of 8:00 or better right now. To improve, I would suggest doing 20 - 25 mpw, with a long run of 8 or more miles and, down the road a couple months, one speedwork day per week. Work on building your weekly mileage first, then speedwork. Your long run should be at a somewhat slower pace. Speedwork can be intervals or tempo. Alternating the two might be good as you introduce yourself to doing these workouts. Work more on short intervals - 200s, 400s, and some 800s. Again, based on a current 8:30 training pace, 6 or 8 months of this will likely get you into the low 7:00 range, maybe better, depending on your natural talent. At that point, depending on your goals and where you are at in achieving them, you could go to two speedwork days a week and possibly a little more mileage.
Go here: http://www.halhigdon.com/5K%20Training/5-Kinter.htm and look at the plan and the explanations below it. Then go to the Advanced plan (there's a link on the page) to compare. You can probably work toward the Intermediate plan now and possibly the Advanced later, if desired. These plans give you a pretty good idea of what you need to do to improve. For paces on your runs, you can use the McMillan Running Calculator (http://www.mcmillanrunning.com/mcmillanrunningcalculator.htm). You can use your training times since you don't have a recent race time.
How fast can you get? Well, there are some on this board who run sub 20s. Others (me, for instance) are happy with low 22s (though I'm nowhere near that anymore). 8:00 pace is 24:51.
Len