Accused of working to overthrow the state, the group had protested the government's handling of a massive toxic waste spill in 2016.
Nguyen Phu Trong would be the first since Ho Chi Minh to hold both jobs at the same time.
Prison authorities refuse to let Tran Thi Nga see her husband and children, citing violations of prison rules.
The men are found guilty of disrupting public order for attacking police with bricks, rocks, and Molotov cocktails.
The five, members of the Vietnam National Alliance of Self-Determination, have been charged with activities aimed at overthrowing the government.
Doan Khanh Vinh Quang had critized Vietnam's ruling Communist Party and government online, authorities said.
Tran Dai Quang, who had previously served four decades in Vietnam's Ministry of Public Security, had jailed scores of political dissidents and rights advocates.
Dao Quang Thuc had called on Facebook for environmental protections and his country's territorial rights in the South China Sea.
Duong seeks appeal of “disturbing public order” ruling by court in Bac Ninh province.
Nguyen Van Tuc, a member of the Brotherhood for Democracy, had criticized the government in writings online.
Nguyen Trung Truc, a member of the online Brotherhood for Democracy advocacy group, had been convicted of working to overthrow the government.
Vo Tan Minh, a drug trafficking suspect, died in Sept. 2017 after being beaten and kicked in a cell by detention center guards.
The move is seen as a further attack on freedom of expression.
Relatives seeking answers are sent first to one place then another by police, family members say.
The clash comes two days after residents block a highway to protest operations at a polluting waste-processing plant.
The democracy advocate is protesting police pressure to plead guilty in exchange for amnesty.
Tran Huynh Duy Thuc is now entering the third week of his strike and is growing weak, his brother says.
Hoan Tuan Long died Aug. 24 showing signs of severe physical injuries, his wife says.
Her editor says Trang has health worries and is constantly on the move to avoid police.
Phan Thi Dao has been in jail since her arrest in April 2017.
Tran Thi Nga gets death threats from cellmate, while Tran Huynh Duy Thuc refuses food to protest pressure to confess in exchange for amnesty.
Singer Nguyen Tin and activists injured after police raid his performance in a small Ho Chi Minh City coffee shop.
Le Dinh Luong had written Facebook postings protesting a toxic waste spill and calling for a boycott of parliamentary elections.
Nguyen Ngoc Vinh refused to write a ‘self-criticism’ after penning an article deemed divisive.
Michael Nguyen disappeared in Vietnam on July 6 and was confirmed detained more than three weeks later.
Human rights advocate Huynh Thuc Vy had ignored previous summons from police to come in for questioning.
Nguyen Trung Truc's eyesight and physical strength are in decline following his arrest, a fellow activist says.
Guards have warned them that they will be subjected to sexually transmitted diseases, their lawyer says.
Priest says film on the prominent political prisoner drew 1,000 from his parish in Nghe An province.
Hua Hoang Anh died after a police interrogation over his role in rare large-scale protests.