The rights group said the death sentences were issued following an unfair trial during which only weak evidence was presented. The five have been charged with sending videos and pictures to an exiled opposition group, the Mujahedin Khalq Organization (MKO), which is on the U.S. list of terrorist organizations.
A campaign spokesman, Aaron Rhodes, said that the death sentences were aimed at "intimidating" the protest movement.
A lawyer who represents political prisoners has told the group that when the authorities accuse political prisoners of being members of opposition groups such as the MKO, it becomes impossible for the Iranian media, human rights lawyers, and defendants' families to publicize their cases.
"This gives the authorities a free hand to use such punishments to terrify government critics and dissidents," the lawyer said.
Several hundred people were arrested in Tehran and other cities following street protests over the reelection of President Mahmud Ahmadinejad in June 2009 and put on trial in procedures condemned by right groups as a parody of justice.
While some have been released, many remain in jail where they are reportedly facing difficult conditions.
-- Golnaz Esfandiari