Police were still looking for the suspect, who used an AR-15-style rifle in the shooting late on Friday, San Jacinto County Sheriff Greg Capers said.
Authorities have charged Francisco Oropeza, 38, with five counts of murder and were searching for him in a nearby wooded area, Capers said.
"Our number one priority is like it's always been since the early morning hours of this morning, late late last night has been to locate this suspect and put him behind bars where he belongs," Capers said.
Officials from Capers' office received a call from Cleveland about harassment at around 11:31 p.m. local time but when they reached the scene they found several victims who had been shot, he said.
There were a total of 10 people in the house when the gunman got in and started shooting, said Capers, five of whom survived.
Enrique Reina, the foreign minister of Honduras, said the Honduran consulate was in contact with the authorities in Texas.
The suspect stepped out of his house on Friday night and started shooting off rounds in his yard which is when some of the victims stepped out to confront him, Capers said.