As a guy who has run basic training for recruits in the military, I would say the most common is shin splints (by far), followed by tendonitis, plantar fasciitis, IT band syndrome, and in exceptionally rare cases, compartment syndrome (although I have seen it, and this requires surgery to correct).

Prevention is key for these-- particularly by familiarizing your body with the loads incrementally. While some may have the aerobic fitness to complete a 5k (even if they're new to running-- a cyclist or swimmer, perhaps) the musculo-skeletal adaptations involved with consistency haven't occurred yet, and injury is a lot more likely. Even elite runners, when they're "getting back into it" start with alternating run-walks to avoid the "too much, too fast" loading.

Most of these can be addressed by seeing a physiotherapist, and normally involve cutting mileage or pace significantly and/or strengthening weak supporting muscles.