What could cause daily eye discharge in a 5 month old?

The most common cause of recurrent discharge from the eyes of a 5 month old is a nasolacrimal duct obstruction (blocked tear duct).  This results in eyes that appear wetter than normal and often results in tears rolling down the cheek during the day and discharge from around the eyes, especially when the child first wakes up.

In the majority of children, the problem will resolve itself  by the time the child is 1 year old.  Antibiotic eye drops are often used when the discharge is present throughout the day.  If the problem does not resolve after a reasonable time, a surgical procedure is available to correct the problem.