The 44-page complaint filed Tuesday states that Maduro had an elite security force called Special Action Forces, or FAES, execute the men between 2017 and 2020.
It says the victims were among thousands killed under Maduro's command by units including FAES, which dissolved in 2021 after complaints of human rights abuses including from the United Nations.
Maduro is currently in a New York jail awaiting trial on criminal charges of drug trafficking after the US military removed him from office in an extraordinary raid in Venezuela in January.
During his 2013 to 2026 presidency, he was widely accused of using political repression to cling onto power.
More from WorldThe civil lawsuit, filed in federal court in Brooklyn, says the alleged assassinations of the five young men followed a familiar pattern of extrajudicial killings under Maduro.
It describes how FAES officers came to the victims' neighborhoods in early morning, wearing all black with faces covered, and separated the men from their families before shooting them. Officials then fabricated narratives that the victims had "resisted authority."
"Maduro used FAES as a political instrument and mechanism of social control to violently suppress dissent, terrorize low-income neighborhoods, and eliminate political opposition," the lawsuit states.
"In fact, FAES is widely considered a 'death squad' or 'extermination group,'" it adds.
The lawsuit says a biased Venezuelan judiciary has prevented accountability for the killings.
The families, whose identities are protected for safety reasons, have sued under the United States' Torture Victim Protection Act and are seeking financial compensation from Maduro.
The former strongman is expected to seek immunity as a head of state, The New York Times reported.
In his criminal case in which he is charged alongside wife Cilia Flores, Maduro has declared himself a "prisoner of war."
He has pleaded not guilty to the four counts he faces: "narco-terrorism" conspiracy, cocaine importation conspiracy, possession of machine guns and destructive devices and conspiracy to possess machine guns and destructive devices.
