The five are suspected members of a branch of ISIS-linked Jamaat-ul-Mujahideen Bangladesh or JMB group.
"They including a father, his wife and their two sons and a daughter," senior police officer Sumit Chowdhury told news agency Agence France-Presse(AFP).
Police surrounded the house after receiving intelligence inputs. They said two of the family members came out and threw grenades, and another person attacked a fire service officer with a sharp rod. Local reports said two policemen have been injured in the incident and are hospitalised.
According to local media, hours after the blast, a woman, who was seen sitting on the field nearby, surrendered. She is reportedly another daughter of the house owner Police said they rescued her two young children who exited the premises before the terror suspects came out.
On Sunday, two suspected terrorists blew themselves up in "suicide blasts" when security forces raided their hideout. In March, Bangladeshi police conducted a series of large- scale operations, in which at least 17 suspected terrorists were killed.
Bangladeshi security forces have been looking for members of Jamaat-Ul-Mujahideen Bangladesh which was behind the Dhaka bakery attack in July last year that killed 22 people. The police and Army have killed 70 suspected terrorists and arrested hundreds since then.
(With inputs from agencies)