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.
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"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.
Those blasts and subsequent bombings later that year, that killed 28 people, shook the mainly moderate Muslim nation of 160 million people whose government had earlier denied the presence of any militant groups.
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 Shia 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.
Sunni-majority Bangladesh has been plagued by unrest in the last three years, and experts say a long-running political crisis has radicalised opponents of the government.
Since November at least five JMB commanders have been killed in shootouts with security forces, police say.
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