It marked the latest in a series of such attacks since Nairobi sent troops into Somalia to fight the Islamist Shebab.
"There was an explosion in a club in town shortly before midnight (Saturday) and five people died," a senior police officer at Northeast provincial headquarters told AFP.
"After the explosion in the club there was shooting outside and people were running all over. It appears they targeted New Year celebrations," the officer added, asking not to be named.
Regional police chief Leo Nyongesa told AFP: "We are investigating. We are looking for the attackers."
Residents voiced fears that the attackers might have been Somali Shebab insurgents or their sympathisers, intent on creating a divide between Christians and Muslims in the region.
Peter Mwathis, a guard who was wounded in the attack in the garrison town, described the assailants as four men dressed in military uniform.
"I was confronted by a man in full Kenyan army uniform who asked me to open the gate. When I saw he was holding a grenade I ran into the bushes," he told AFP from his hospital bed.
"Then I heard a big blast and the place was sprayed with bullets. I thought I had escaped but later on I felt a sharp pain in my chest and realised that it was a bullet wound.
"I heard people cry loudly as more bullets rent the air targeting those fleeing from the bar," he added.
Mohamed Abdikadir, the provincial director of public health, said a total of 21 people injured in the blast are being treated at Garissa hospital; two are them are in critical condition while the rest are out of danger.
There were unconfirmed reports of two police officers among the dead, one who was shot at the entry to the bar and the other who was hit in a taxi a short distance away.