I'm a slow runner too... and I've had the same concerns as you, since I want to do the Run for the Cure at the end of September for my first 5K.
I'm currently at 5.1K in 36 minutes. I figure that although it's pretty slow by an athlete's standards, it really isn't too shabby, since when I first started four months ago (walking and running combined), it took me 55 minutes to go 5.2K (yes, I was a very slow walker, I'm short, and there was the hill of death on that route, in my defense). I'm just competing against myself. Every week, I try to shave a little bit of time off of my previous time, and it's working!