Four people were killed at the scene about 50 miles from the Mexico border and a fifth person died at a hospital in San Antonio, the sheriff said.
"This is not unusual", Boyd said.
The sheriff told the San Antonio NBC affiliate that it was "good police work" that led to deputies being involved in the chase. "There needs to be censors, there needs to be other things integrated to be able to protect our borders".
The sport utility vehicle skidded off the road and then attempted to get back onto the highway, but the driver overcorrected and the vehicle flipped over, ejecting several people, Boyd said. One person died upon arriving at the hospital, reports ABC News.
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Footage of the crash showed four bodies on the ground, the charred Chevrolet and several Border Patrol vehicles at the scene.
He added: "This is a ideal example of why our borders need to be secure". There were 14 people in the Suburban, including the driver, according to the department.
The other 12 passengers were undocumented immigrants, Boyd said. Border Patrol agents stopped two of the vehicles and made multiple arrests, but the third vehicle continued, the statement said.
The sheriff said it was just the latest in a series of police chases involving human and drug smugglers in the Big Wells area.
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The Trump administration has said tougher immigration policies are needed to deter immigrants from entering America illegally.
Boyd added that a wall is not the only answer.
Twelve immigrants were ejected and four died at the scene when the auto crashed and rolled over, according to Boyd.
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