Allen police discovered the bodies while performing a welfare check at a home around 1:00 Monday morning.
The names and ages of the victims have not been confirmed, but police said they included a grandparent, two parents, a sister, and the two teen boys.
Police Sergeant Jon Felty said it appeared two teenage sons agreed to die by suicide and kill their family members.
Police believe the killings may have happened over the weekend.
Felty said the family apparently emigrated from Bangladesh.