What you really need to do for clothing, don't try to spend a lot on running gear just yet.
The essentials are:
gloves to cover you knuckles, especially
hat: the dollar store is great
fleece sweat shirt: old navy is cool
good pair of socks: REI has a ridiculous amount for ever need
and your running shorts that you picked up at your favorite Luke's Locker or Run On! Store.
Remember to keep your ears covered and your chest covered. Just like crazy fire it will rise out through your head so keep the heat in by just wearing a hat. Don't over-dress with sweat pants, you will become overheated and that will mess with the leg muscles and your internal heating mechanisms. So, by keeping it simple, you will stay warm. Not to mention, runners have to keep it light because time is of essence. If you are training to run in a very humid environment like Jamaica then a good thing to do is wear the plastic outfit. But, remember a 5k is only 3.2 miles- so keep it light and get to the finish fast!
Race and training are similar because you want to train some days just like your race day so dressing the same for training a few days a week will eliminate guessing on race day.