Connolly was not punished at the time by the referee, but the incident was caught on video.
"The FA claimed the standard punishment of a three-match suspension would be clearly insufficient given the nature of the offence," read a statement on the FA's official website.
"Connolly accepted the charge but denied the standard punishment was clearly insufficient.
"However, the Independent Regulatory Commission found in favour of The FA and ordered that Connolly be suspended for five matches, commencing with immediate effect."
Connolly is able to appeal against the five-game suspension.