Seems to be a lot of us Michigan (or former Michigan) types on this thread. 
Regarding the C25K program, just keep at it until you can successfully complete the first week, and then repeat weeks as necessary until you can complete the entire routine. A few pointers:
- Many folks doing C25K for the first time run too fast during their running segments; when the program says "Run", you should think, "Slow Jog" (Slog for short).
- Running is often as much a mental thing ("I couldn't possibly run more than five minutes...") as it is a physical thing. The only thing which will allow you to run more is to, ummm, run more.
- When the program says "Rest", please rest, your body needs time to recover from this new activity; rest is equally important to the running and walking.
As for the 5K on 31-May; you should be okay to complete it, however, you may need to walk portions. Don't be discouraged if you need to do some walking; think about it this way, you'll still be faster than folks sitting on the proverbial couch.
Keep us posted on your progress.