The main problem with eating before running is nausea and burping up your breakfast during your race. Once the food moves from the stomach to the small intestine, most people are fine (some people experience cramping, but this is uncommon in healthy runners). The stomach usually takes 30-60 minutes to empty, and it empties more quickly with a liquid meal than a solid meal (PubMed).
In endurance running, your main nutritional concern is carbs, because your body has relatively small stores of them. Runners often load up on carbs in the days before long races to fill up these stores as much as possible. Full stores can last 30-90 minutes, depending on intensity (about.com), so maybe that covers you for a 5k, maybe it doesn't, but why not give yourself a little extra fuel, just in case?
Before a race, I usually go for something like a banana smoothie made with yogurt about 45-60 minutes before the race. It is high in complex carbshas a low glycemic index, which means it will give you a sustained delivery of glucose throughout your run (rather that a spike and a drop). Bananas are also high in potassium, which is important to prevent muscle cramps (health911). If you want to really step up your game, caffeine is an effective performance enhancer, which is thought to work by increasing muscle contractility, mental alertness, and pain tolerance (Current Sports Medicine Reports). According to the article I cited its diuretic properties (makes you have to pee more) are not significant enough to dehydrate you.