I have to say, I'm pretty surprised by the crappy responses so far.
There are 2 things that will keep you from running faster in a race: 1) Running out of energy, 2) Building up lactic acid faster than your body can remove it by running too fast.
Your body has enough energy stored in it to run for 90 minutes so #1 is a non-issue for the 5k. We also don't really need to worry about warming up too much since a long warm-up + 5k race still won't deplete energy stores. In order to do run your fastest in such a short race you need to make sure the lactic acid removal system in your body is running at 100% when the gun goes off. If it isn't then you will waste precious time warming that system up, or your body will get behind on lactic acid removal and never catch up.
The finer details of a warmup are up to you, but it should include a slow jog to get thing started anywhere from 15 - 30 minutes and later involve 3 - 5 x 2min at 90%+ effort and 4 - 6 x 100-150m strides at race pace. You should be sweating and your heart should be elevated after all of this. Shoot to finish your w/u about 5 minutes before the start so your body doesn't really have time to shut down lactic acid removal, but enough time to feel refreshed for the gun.