A court in the southeastern district of Rangamati convicted the five members of banned group Jamayetul Mujahideen Bangladesh (JMB) over two explosions in the area, police Inspector Mominul Islam said.
"Six JMB militants were charged with the bombings. One was acquitted and five others were sentenced to ten years in jail," Islam said.
The twin blasts were part of synchronised bombings carried out on August 17, 2005 across all Bangladesh cities and almost all districts that left two people dead.
Hundreds of suspected militants were later arrested and JMB's top leaders executed in 2007.
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In recent months, police have blamed a regrouped JMB for an upsurge in deadly violence, including the murder of two foreigners last year and deadly attacks on minority Shiite and Sufi Muslims and Christians.
The government has rejected the Islamic State's claims of responsibility for some of those attacks, saying IS has no presence in Bangladesh.
Since November at least five JMB commanders have been killed in shootouts with security forces, police say.