One person was injured in the home in the 600 block of Lone Star Park Lane, a little more than 35 miles north of Fort Worth.
No suspect is being sought, authorities said.
Authorities said later that the dead included two adults and three children, and that they were shot.
The Tarrant County medical examiner's office identified the adults as Justin Painter, 39, of Fort Worth, and Seth Richardson, 29, of Lancaster, South Carolina. According to the medical examiner's post, Painter and Richardson were found in the bedroom of the residence and pronounced dead about 8:35 a.m.
The medical examiner's office identified the children as Odin Painter, 8; his sister, Caydence, 6; and Drake Painer, 4. They were found in a living room.
Investigators were searching through a red Ford Focus with South Carolina license plates that was parked at the residence.
Capt. Orlando Hinojosa with the Denton County Sheriff's Office said the deaths were the result of a shooting. Fort Worth media partner WFAA-TV said investigators are treating it as a murder-suicide.
"The shooter was a male," Hinojosa said. "He died from a self-inflicted gunshot wound."
Hours after the shooting, authorities were removing pets from the home.
Numerous law enforcement officers and vehicles could be seen outside the residence and a large area around it was roped off with crime scene tape.
Hinojosa said authorities had received a burglary call shortly before 8:30 a.m. at the residence.
Ponder ISD Superintendent Bruce Yeager said school records did not indicate that it was the home of any students or staff in the district.
"My prayers are with our community and each of you," Yeager said in a statement released to parents in the district.
Yeager said in a telephone interview he had been in contact with Ponder police, and a lockdown was not needed.
"I am certain people will be concerned about the safety of their children as events of this nature heighten awareness," Yeager said in the prepared statement. "Be assured that as a district we were taking precautionary measures and seeking information to ensure the most safe and uninterrupted school day possible."
In Ponder on Wednesday, residents said they'd been discussing the event all day, mainly getting scanty information from local media sources, along with swirling rumors from their friends and neighbors but few hard facts.
Neighbor Natalie Carr, who lives across the street from where the shooting occurred, said three children lived in the home.
Carr said she only saw a woman who lived at the home in early April at a garage sale.
Another neighbor Dianna Booker said she didn't know the people.
"I didn't even know if they owned the house or rented," Booker said. She said she'd been in the area for 16 years.. "I felt like I lived in a safe neighborhood."
Other neighbors agreed.
"It's sad," neighbor Mark Downing said Wednesday. "It shouldn't happen to nobody."