The five - four of whom were released in April, May and August - were immediately locked up in Yemeni prisons pending trials, al-Alimi told parliament, without specifying what charges they would face.
"Four of the detainees who were handed over by the United States this year were accused of belonging to an international terror group, and the fifth, who was handed last year, was accused with involvement in drug cases," al-Alimi said.
Al-Alimi said the trial of the five would begin once the United States had sent through their files.
Yemen previously received from the US authorities a list of the names of 104 of its nationals being held in Guantanamo and another two at the US base of Bagram in Afghanistan.
Sanaa has long been trying to secure the handover of its nationals from Guantanamo for trial in their own country.
The United States is holding an estimated 600 suspected al-Qaida and Taliban fighters at Camp Delta, a high-security camp in Guantanamo Bay, and has faced strong international criticism of the legal limbo that has left the prisoners without access to legal representation.
With US backing, Yemen launched its own crackdown on Islamists after the 11 September, 2001, attacks in the United States.