They were indicted on Thursday and their case will be processed in the “shortest possible time”, the chief justice of Fars province told the judiciary's Mizan news agency.
Thirteen people were killed when gunmen opened fire on worshippers at the Shah Cheragh mausoleum on October 26 in an attack later claimed by ISIS.
The five accused, who will be tried by the Shiraz Revolutionary Court, face several charges including membership of ISIS and “corruption on earth”. The latter almost always carries the death sentence. News of their indictment came at the end of the traditional 40-day mourning period in Iran.
ISIS has carried out several attacks in Iran, including a 2017 bombing near the tomb of Ayatollah Khomeini. Tehran executed eight men over the 2017 attack, which also targeted parliament.
The attack came amid nationwide demonstrations that have posed the biggest threat to Iran's ruling clerics since the 1979 revolution. Some supporters of the protests have questioned whether it was an attempt by the government to distract the public amid anger over the death of Mahsa Amini, 22, who died in the custody of the morality police.
Iran on Thursday carried out the first execution of a protester, prompting Germany to summon the Iranian ambassador, a diplomatic source told AFP.
Mohsen Shekari, 23, who was hanged, was among thousands arrested over the protests, including svereal who also face the death penalty. Activists estimate that as many as 500 people have been killed in a crackdown on the protests by the Islamic Revolutionary Guard Corps and other state forces.
His funeral on Friday was guarded by security forces, Radio Farda reported.
Activists said he was laid to rest in Iran's largest cemetry, Tehran's Behesht-e Zahra, amid a "heavy security presence" and only a few family members.
Footage shared widely on social media showed a woman reported to be his mother wailing in the street upon learning of his execution.
Meanwhile, Iran's top Sunni cleric denounced Shekari's death, telling worshippers in Zahedan the protests "will not be extinguished by killing people."
The man's execution was "incorrect" and against Sharia law, said Molavi Abdolhamid
Iran, which has one of the world's highest execution rates, has continued to pursue capital punishment despite condemnation over previous killings of high-profile citizens, including journalist Ruhollah Zam.
Prisoners on death row are usually hanged after one day in solitary confinement, often with no notice given to their families.
Tehran is routinely accused of denying due legal process to people accused of crimes, and often hands down charges of espionage and “corruption on earth” to those who speak out against the regime.
Its human rights record will elicit fresh EU sanctions, France said on Thursday.
The EU will discuss new measures in response to Tehran's crackdown on protesters and its drone supplies to Russia, French foreign ministry spokeswoman Anne-Claire Legendre told reporters.
Ireland said the sanctions were likely to be announced on Monday during a meeting of the EU's Foreign Affairs Council.
The EU has already sanctioned Iran for its support for Moscow's invasion of Ukraine and violent response to the protests at home. Washington has also imposed several rounds of sanctions since September, targeting regional and federal officials responsible for the crackdown — including in Kurdish and Baloch areas which have seen significant bloodshed.
World Cup death
Meanwhile, Iran has arrested a police chief over the death of a man who was killed while celebrating Iran's World Cup loss against the US.
State news agency Irna said more than one person has been arrested over the death of Mehran Samak, who was shot while honking his car horn after the national team's defeat. He was mourned by childhood friend and World Cup midfielder Saeid Ezatolahi.
Several people have been arrested as part of an investigation into his death, according to Irna, which quoted a local police official.
It claimed Mr Samak was shot dead “during a gathering”.
Among those arrested is a local police chief, a family lawyer told the semi-official Tasnim news agency.
Bandar Azali police commander Jafar Javanmardi was placed in pretrial detention a week after Mr Samak's death, lawyer Majid Ahmadi said.
Iran's loss to the US was widely celebrated by anti-government football fans, some of whom have been harassed in Qatar and prevented from displaying pro-protest slogans.
The defeat was marked by fireworks in the hometown of Ms Amini, where the protests began following her funeral in Saqez in September.