Hydration is not really important in a 5k run per se. Providing you are properly hydrated most of the time you will not need to hydrate during a 5k or probably also even a 10k run.
However having said that you need to note the following.
1. You need to be properly hydrated much of the time. This is just good for you, it is a natural state to be in. Your body is made of water and it definitely needs water to properly function.
2. During your training and after your training you need to maintain proper levels of hydration. This will probably make you feel better (better able to handle an occasional night on the town as well!).
3. Being properly hydrated will help your recovery from training.
4. Being properly hydrated will probably usually PREVENT your body to going into an unnatural state of water-retention. Not nice.
What is properly hydrated?
a. If you are thirsty then you are dehydrated to some degree already. Your body tells you it needs water a bit too late.
b. Unless you’ve eaten something wierd your urine will be colourless or very light yellow coloured. That is the scientific test of hydration !! Well, as good as you’ll ever need!
c. 3 litres per day of bottled water is too much. Providing you take in water through other food I would say that 1-2 litres of water by itself as a drink is sufficient. If you do strenuous training you need to replace WEIGHT lost from sweat whilst exercising (ie weighing yourself immediately afterwards) with an equivalent weight of water or some isotonic drink. (1litre of water weighs 1kg, very clever this metric stuff)
d. If you drink MUCH MUCH too much you can wash the salts out of your body and die!