So vague...?!
What pace? Do you want to win, being all that competitive?
Howe fit are you?
5km in a month, from zero, is easy.
Should take about 30 minutes at a slow steady pace. You probably should be able to do 3km on your first run, and add 0.5km per week with 2 runs per week.
I find it takes about 10-12 weeks to get up to 10k (~50-55 mins) from zero.
@pinkfloyd, I do a bit of cycling, not much though, but different muscles, more lung work with running also, but overall cycling is more difficult. If you do go for a run, I suggest reps instead of just doing a long run. Be aware though it could take you a few days to recover from your first run.