My 5yr old has a slight cough in the morning and then nothing all day. He is fitting fit ehat could be causing this?

Allergies/dry throat. Do not understand the. He is fitting fit....But cough only in the morning and then fine all day could be related to a dry throat or allergies. Sometimes there are allergens in the child's room...Like stuffed animals in the bed, carpet, dust mites. Generally it is not a big issue unless it is interrupting sleep, affecting appetitie or going on for a while. Ask your pediatrician as well.
Congestion. Often children who are congested with mouth breath at night and wake up with dry throat causing cough. Does he sleep well through the night? Or is he a snorer. Best to discuss with your pediatrician whether his tonsils are enlarged and if his adenoids could also be enlarged. No treatment is necessary unless this is disrupting his life.