Could my 5 month old have pink eye?

It is very possible....it is very common and very contagious! Wipe your son's eyes with warm water on a cotton ball or soft washcloth. Discard the cotton ball immediately and/or launder the washcloth immediately,, use different ends of the wash cloth for each eye and make sure you wash YOUR hands thoroughly. If you are breastfeeding put a small amount of breast milk in the corner of each affected eye..My little one had this at 2 months...these steps cleared it up..it's easier than the ointment they may give you, but if your not breastfeeding you will need to use the prescription. However you should contact your doctor because there are two different types of pink eye (conjunctivitis), one viral and one bacterial...Best of luck!