Congrats for committing to a 5K! I love running and it is a great way to get your body really healthy.
Google "Couch to 5K"
and you will find a bunch of different training programs designed to gradually and safely increase your running distance.
Be sure you are wearing good, appropriate footwear. If your shoes are worn, replace them now, not the week before the race. The best bet is to go to a specialty running store where the staff can fit you for shoes appropriate for your feet and gait. It can be a big financial commitment, but it helps avoid injury.
Remember to stretch. I do dynamic stretches
for a warmup and regular ol' static stretches
when I cool down. Stretching is sooooo important for avoiding injury. I cannot emphasize it enough.
Most of all -- have fun! Running can be hard when you are getting started. I remember some really tough days chugging along, carrying a Walkman (yep, I started that long ago). But once you get into your groove you just may find that you love it!