The attack took place late Thursday as seven vehicles carrying the paramilitary gendarmerie officers were on patrol in Ocotlan, Jalisco state, federal police said.
Eight other officers were wounded, including one in serious condition in the town of 93,000 people.
It was the deadliest shooting for the gendarmerie, a 5,000-strong unit modeled after European military-like police forces that President Enrique Pena Nieto launched last year to protect key economic sectors from organised crime.
"We have regrettably had minor losses of one officer in some other events," but never so many in a single attack, a federal official told AFP.
A police statement said the officers were on patrol around 9:15 pm local time when a pick-up truck approached the convoy and "without uttering a word, one of the individuals pulled out a large weapon and shot at the federal agents."
The officers shot back but more gunmen arrived in about 10 other vehicles. The gendarmerie commander said the shootout lasted 30 minutes and took place on several streets.
"As a result of this clash, we report the deaths of five gendarmerie division officers and three civilians whose bodies had cartridge belts and tactical equipment and who presumably are part of organised crime," the statement said.
The suspects kept shooting as they fled the scene, leaving bullet holes in vehicles parked on several neighboring streets.
Authorities found seven "large weapons" -- a term usually used to refer to assault rifles -- and four grenades. The suspects left behind five vehicles.
The statement did not specify the criminal gang affiliation of the suspects, but the region is home to the Jalisco New Generation drug cartel.
The group emerged in 2010 after the death of Ignacio Coronel Villarreal, alias "Nacho Coronel," the top leader in Jalisco for the powerful Sinaloa drug cartel.
Interior Minister Miguel Angel Osorio Chong expressed his condolences, while federal police chief Enrique Galindo urged any witnesses to report information through the 088 emergency telephone number.
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