Nguyen Ngoc Nhu Quynh was 16 months into a 10-year anti-state propaganda sentence.
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.
