Looking for a race? Here is a 1/2 marathon in March in beautiful Grosse Ile. http://www.outruncf.com/ Rock CF is a race dedicated to improving the quality of life for people with Cystic Fibrosis. The founder of the race is a remarkable woman who was diagnosed with CF when she was a toddler. Her parents were told that she wasn't going to live to be an adult, but at 28 years old she has found that running makes her quality of life better.
Five months is plenty of time to train for a 1/2 from any starting point. If you are not running now or are only running short distances use the first 4-8 weeks to build up to 5k. There are many training schedules out there for this distance. My favorite is from Hal Higdon http://www.halhigdon.com/