Marines were on patrol in the city when heavily armed civilians who were travelling in several vehicles opened fire, prompting the troops to hit back.
Marines were on patrol in the city when "heavily armed" civilians who were travelling in several vehicles opened fire, prompting the troops to hit back, the Sinaloa state prosecutor's office said.
The five suspects were all men who were wearing bulletproof vests and were armed with AK-47 and AR-15 assault rifles, the office said in a statement.
The attack took place as Culiacan hosts the 2017 Caribbean baseball championship, which includes Cuba, Puerto Rico, The Dominican Republic, Venezuela and Mexico.
Ten other people were killed in three separate shootouts in the city over the weekend, officials.
Culiacan is the capital of Sinaloa state, the bastion of Sinaloa drug cartel leader Joaquin "El Chapo" Guzman, who was extradited to the United States last month.
Sinaloa is among the most dangerous regions in Mexico's drug war, which has left tens of thousands of people dead nationwide since 2006.
Overall murders rose for the second year in a row last year, surging from 17,034 in 2015 to 20,789 in 2016.