Government troops killed two people in a shootout in the town of Tuzantla, and two others were killed when their car crashed during an escape attempt, the state prosecutor's office said.
In the town of Benito Juarez, troops killed a member of a drug gang in a brief firefight, the official report said, adding that a kidnap victim was freed after that encounter.
All five of the dead were alleged to be members of the La Familia Michoacana cartel and a gang that calls itself the Knights Templar.

Michoacan, a state on Mexico's Pacific coast, holds local elections November 13 in which President Felipe Calderon's sister is running for governor as the candidate of the ruling National Action Party.
Calderon on Monday acknowledged that the issue of corrupt police remained a critical problem.
"This is a vital security issue for the country. Let's be frank. There are not trustworthy police at all levels," Calderon said at a national public safety council meeting.
"It would be better to have fewer police on the job and have them all be trustworthy than a throng of police, many of whom are involved in crime," he stressed.
There has been a surge of violence, including three clashes on Friday that left 15 dead, which has raised concerns among political parties with candidates in the race.
Drug-related violence has left 45,000 dead in Mexico since December 2006 when Calderon launched a military campaign to uproot the cartels.
In a separate part of the country, armed men kidnapped four people over the weekend in Cancun, including a Mexican businessman, his girlfriend, their physical trainer and an auto mechanic, authorities said.
There were 1,847 kidnappings in Mexico in 2010, and in 136 cases the victims were killed, according to a non-governmental organization that tracks public security issues.