In a statement, they also called on Egyptians not to recognize the presidential vote's outcome if it goes ahead.
The incumbent general-turned-president Abdel Fattah el-Sisi is so far the only candidate in the race for the March 26-28 vote. He can win a second, four-year term if he secures the support of five percent of registered voters, about 60 million people.
All potentially serious challengers to him have been arrested, forced out or quit the race.
Sunday's statement by the five opposition figures is a bold move that could be perceived as an attempt to derail the electoral process by authorities that have shown little tolerance for dissent under Sisi. It is also likely to encourage more expressions of discontent over what critics see as the president's increasingly authoritarian traits.
Sisi led the 2013 ouster of a freely elected but divisive president, Mohammed Morsi, and has since overseen what is perhaps the largest crackdown in the country's living memory. Thousands of Morsi supporters have been jailed, along with secular activists. Most critics in the media have been silenced, the work of rights groups restricted and scores of online news sites blocked.
"We call on our glorious people to entirely boycott these elections and not to recognize whatever outcome they produce," said the statement. "This is not only in response to the absence of an electoral contest, but rather out of concern that this policy clearly paves the way for amending the constitution to remove the limit on presidential terms," it said, alluding to the constitutional ban on presidents serving more than two terms. The statement also called on "active opposition forces" to form a coalition to study the "next choices and steps."
The signatories of Sunday's statement include 2012 presidential candidate Abdel Moneim Aboul Fotouh, former lawmaker Mohammed Anwar Sadat, who quit the race saying he feared for the safety of his supporters, and Annan's top campaign aides Hazem Hosny and Hisham Genena. The military arrested Annan last week, accusing him of incitement against the military and forgery.
Issam Heggy, a scientist and former presidential adviser, also signed the statement.
Earlier on Sunday, eight local rights groups expressed their "extreme denunciation" of an attack on Genena, saying it was part of a pattern of retaliations against would-be presidential candidates and their supporters.
Lawyers for Genena said he suffered serious injuries to the face and leg during an apparent kidnapping attempt outside his suburban Cairo home Saturday. They said three men armed with knives tried to force him into one of their two cars when passers-by rushed to his rescue.
Police say the incident began when Genena hit a pedestrian while driving his car. A brawl then ensued between Genena and the victim's friends, who allege in a complaint that the 63-year-old former judge, his wife and daughter assaulted them.
The statement by the eight groups, which include the Egyptian Commission for Rights and Freedoms and the anti-torture and rehabilitation Nadim Center, said "revenge acts" have targeted anyone daring to challenge Sisi in the upcoming elections.
In 2015, Genena claimed that corruption was costing the country billions of dollars. A pro-government daily quoted him as saying that Egypt lost 600 billion pounds or ($67.6 billion) in corruption in 2015 alone. He later said he was misquoted and that his remarks referred to the last four-year period. Sisi dismissed him in 2016, following an investigation that hurriedly concluded that he had misled the public.