Police responding to the Retama Manor Nursing Center in Robstown at 7 p.m. found two men and a woman shot to death, the television station reported.
Police also responded to a call at what they said was the suspect's home, where two men were found dead, KIII reported.
Police believe the suspect killed the two people at the home before heading to the nursing home, KIII reported.
The shooter was "neutralized," according to police. It is unclear if the gunman was one of the fatalities at the nursing home, KRPC reported.
Robstown is located just west of Corpus Christi.
"Current information will remain scarce because we are looking at a murder investigation and not compromising anything that might impede that investigation," Chief Erasmo Flores said in a statement. "Our hearts go out to the victims' families and the residents, visitors and employees at Retama Manor who experienced this tragedy."
The identities of the victims have not been released, KRPC reported.