Mahsa Amini, a 22-year-old from Iran's Kurdistan province, fell into a coma and died following her arrest in Tehran last week by the morality police, sparking demonstrations in numerous areas including the capital.
Two of the people were killed as security forces opened fire on protesters in the Kurdish city of Saqez, Amini's hometown, the Hengaw Human Rights Organization said on Twitter.
It said two more were killed in the town of Divandarreh "by direct fire" from security forces, and a fifth was killed in Dehgolan, also in the Kurdish region.
Reuters could not independently verify the reports.
There was no official confirmation of the deaths. The official news agency IRNA said there were "limited" protests in a number of cities in seven provinces that were dispersed by police.
State TV said a number of protesters had been arrested but rejected "some claims of deaths on social media" by showing two injured youths who denied reports they had been killed.
In the nationwide condemnations of Amini's death, the Persian hashtag #MahsaAmini reached nearly 2 million Twitter mentions.
The police have said Amini fell ill as she waited with other women held by the morality police, who enforce strict rules in the Islamic republic requiring women to cover their hair and wear loose fitting clothes in public.
But her father has repeatedly said his daughter had no health problems, adding that she had suffered bruises to her legs. He held the police responsible for her death.
The protests have been most intense in the Kurdish region, where the authorities have previously put down unrest by the Kurdish minority numbering 8 million to 10 million.
Hengaw said 75 people were injured on Monday.
A video posted on Twitter by Hengaw showed protesters throwing rocks while a man could be heard saying "there is a war in Divandarreh" and accusing the police of attacking.
Reuters could not verify the authenticity of the video.
Internet blockage observatory NetBlocks reported "near-total disruption to internet connectivity in Sanandaj" - the provincial capital of the Kurdish region - on Monday, linking it to the protests, according to its Twitter account.
While Hengaw reported deadly force by security forces in the Kurdish region, there were no immediate reports of protest fatalities in other parts of Iran.
Videos on social media showed demonstrations in Tehran and spreading to cities such as Rasht, Mashhad and Isfahan.
A video shared by the 1500tasvir Twitter account, which publishes footage sent by its 70,000 followers, showed police cars with their windows smashed in Tehran, as a nearby security forces' vehicle fired water canon towards protesters.
"People throwing rocks have advanced against the police. Death to the dictator!" a woman can be heard saying.
It also shared footage showing what it said was a protest at a Tehran university against the paramilitary Basij, a militia.
Reuters could not independently verify the videos.
It marks some of Iran's worst unrest since street clashes that began in late 2021 over water shortages.
The United States demanded accountability for Amini's death.
"Mahsa Amini’s death after injuries sustained while in police custody for wearing an 'improper' hijab is an appalling and egregious affront to human rights," a White House spokesperson said.
France condemned her arrest, "and the violence that caused her death", the foreign ministry said, calling for a transparent investigation.
Earlier on Monday, Tehran Police commander Hossein Rahimi said "cowardly accusations" had been made against police, that Amini suffered no physical harm, and the police had "done everything" to keep her alive.
"This incident was unfortunate for us and we wish to never witness such incidents," Rahimi said.
The police have released closed-circuit television footage apparently supporting their version of events. Reuters could not authenticate the video.
Offenders against Iran's sharia, or Islamic law, and hijab rules face fines or arrest. But activists have recently urged women to remove veils despite the hardline rulers' crackdown on "immoral behaviour".
Amini's death could raise tension between the establishment and the Kurdish minority.
Iran’s elite Revolutionary Guards have put down unrest in the country’s Kurdish areas for decades, and many Kurdish activists have been sentenced to long jail terms or death.