Four were arrested for drinking alcohol inside the ground, while another was cuffed for an alleged assault.
The final supporter was arrested for an alleged sectarian breach of the peace.
The Dons netted twice in the first half, with goals from Jonny Hayes and debutant Simon Church. Celtic striker Leigh Griffiths managed to grab a consolation goal in the final minutes of the game.
A Police Scotland spokesman was happy with the conduct of supporters from both sides during the game.
He said: “The official attendance was 19,003 at the match.
“The vast majority of fans who attended the game were well-behaved.”