Gunmen riding motorcycles and bicycles arrived in large numbers in Pallam village, in the Madagali area of Adamawa state, at about 11:30 pm (2230 GMT) on Monday.
The attack was the first in Adamawa this year after a surge in hit-and-run raids and suicide bombings in recent months.
"Five people fell victim to the attack: three were killed and two were critically injured and taken to hospital," said Maina Ularamu, a former Madagali local government chairman.
"On their way out of the village, they ran into a group of vigilantes on patrol in Kuda village, who engaged them in a shoot-out, killing two of the attackers."
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One of the victims was a shopkeeper who was sleeping inside his shop and refused to open the door to the jihadists. He was burnt alive.
A security guard at a medical clinic was also killed after the militant fighters had looted the facility, said Ularamu.
Adamawa was said to have been cleared of Boko Haram in late 2015, after they rampaged across the northeast, seizing towns and territory.
"There is no doubt the attackers came from Sambisa," said Ularamu. "We experience such periodic attacks from Boko Haram, who usually look for food."
The insurgency began in 2009 and has since killed at least 20,000 people and made more than 2.6 million others homeless.
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