Handwritten messages were also found, reportedly threatening the state governor as well as local drug lords.
It was not clear if the discovery of the heads and five decapitated bodies elsewhere in the city was linked to extortion threats against teachers.
Dozens of schools have been closed since last month after teachers went on strike over security concerns.
Police were called to a street in the Garita neighbourhood of Acapulco on Tuesday morning.
There they found a sack inside a wooden crate placed near the school, officers said.
Inside were the heads of five men, as well as the threatening messages.Threats
Police had earlier discovered five headless bodies in another part of the city, left either inside or near a burned-out vehicle.
Acapulco, on Mexico's Pacific coast, has seen several episodes of gruesome violence as drug gangs fight for control of the resort city. Read More