Kelly,
5-600 is a tight budget for any road bike but do-able. Keep a keen eye on the used bike set on eBay and craigslist then pray hard for some good luck. I got tired of waiting and dropped a grand on a new rig- a few years old Team model Raleigh.
If you want a pure commuter consider single speed flip-flop hub with freewheel one side and fixed the other. There are several makes available in your price range.
Good luck
toadster