The London-based group, in a statement issued on Saturday, said four of the men were "detained for their peaceful and legitimate use of the Internet; one is detained for his work in defence of human rights."
Two brothers Muhannad and Haytham Qutaish, and Yahya al-Aws, arrested 18 months ago, face trial on Sunday before Syria's Supreme State Security Court (SSSC).
They were arrested reportedly for sending articles to an electronic newspaper in the United Arab Emirates, Amnesty said.
Student Masud Hamid, who was arrested in July 2003 reportedly for posting photographs onto Internet sites of a peaceful Kurdish demonstration in Damascus, also goes before the SSSC on Sunday.
On Monday, the security court is to try Aktham Naisa on charges relating to his work in defence of human rights, Amnesty International said.
Naissa was a political prisoner between 1992 and 1998 before being detained again on 13 April in the northwestern coastal city of Lattakia. He heads the Committees for the Defence of Human Rights and Democratic Freedoms in Syria (CDHRDFS).
"Over the years, Amnesty International has documented evidence showing how trials held before the Syria's Supreme State Security Court (SSSC) are grossly unfair"
Amnesty International statement
He faces several charges, including carrying out activities that run counter to the country's socialist system. Amnesty said the charges could carry a sentence of up to 15 years.
Naisa is being held in solitary confinement but has been allowed to meet his lawyers and briefly with his family, it said.
"Over the years, Amnesty International has documented evidence showing how trials held before the SSSC are grossly unfair," it said, adding that these trials are not subject to appeal or bound by rules of the Code of Criminal Procedures.