Authorities have not released the family's name, but relatives identified it.
The man and his 16-year-old daughter had found his wife with another man at a store on Friday night, Ed Troyer, a spokesman for the Pierce County Sheriff's Department, told the Tacoma News Tribune.
Troyer said the woman told her husband that she was leaving him for the man she was with. The husband "was devastated," Troyer said.
Investigators believe the father later killed his children and returned to the area near the store looking for his wife. His body was found near the store, Troyer said. No suicide note was left.
On Sunday, the mobile home where the five children, ages 7 to 16, were slain became a makeshift memorial as neighbors left cards and flowers.