A 23-year-old man from the Glasgow area has been charged over alleged sectarian singing and offensive behaviour at the game in Aberdeen and he will appear in court at a later date.
Four men aged 20, 26, 27 and 28 from the Aberdeen area were charged with alleged minor public disorder offences outside the stadium linked to football.
Match commander Superintendent George MacDonald said: “The vast majority of fans followed the advice given and conducted themselves appropriately.
“We are aware of damage to a number of seats in the away support area and the toilet area and inquiries are ongoing along with the club in relation to this.
“A flare was thrown on to the trackside towards the end of the fixture near to the South/Merkland Road stands and we would appeal for anyone who has information in relation to this to contact us or the club as soon as possible.
“The policing operation was assisted by the Police Scotland helicopter and other specialist resources including the horses and we appreciate the support of the overwhelming majority of fans and members of the public in allowing the game to pass safely.”