Two men were arrested before the game at Easter Road in Edinburgh, and three were detained after the 1-1 draw.
Shortly before half-time in the Scottish Premiership match, a supporter was seen going on to the side of the pitch and becoming involved in an exchange with Rangers captain James Tavernier.
A seat was also hurled from the stand.
Police said inquiries are continuing.
Superintendent Barry Blair said: “It is extremely disappointing to see such acts of disorder disrupt a football match and this type of behaviour will not be tolerated.
“Investigations remain ongoing and five men have so far been arrested and charged in connection with incidents that occurred prior to and during the match.
One of the alleged disorder offences includes the use of a pyrotechnic device.