Usually a cough lasting for more than a week alone is not considered chronic. A child of 5 can suffer from an acute upper respiratory tract infection where symptoms of cough can outlast other symptoms such as fever. Giving steam, and throat soothing remedies may help. Does your child suffer from frequent episodes of cough? Have you noticed any seasonal trend or association with exposure to dust or pollen or pet hair. Do you hear wheezing sounds when child breathes. It would be helpful if you consult a physician who can take history and examine and offer better solution.