My kids do the same - it's asthma with them. Their lungs sound okay at dr.'s but it's asthma none the less. For a lot of kids coughing is the only asthma symptom they get - their lungs sound clear.
I would see if they would try ventolin or another asthma med to see if it would help. My 3 kids are all on different meds, we had to try a number of different ones to see what worked.
Good luck!
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5 year old coughing 
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