The fatal crash occurred around noon local time near Big Wells, which is about 100 miles southwest of San Antonio, Dimmet County Sheriff Marion Boyd told reporters at the scene.
Authorities are investigating the scene where a auto full of undocumented immigrants being chased by Border Patrol agents crashed. Border Patrol agents stopped two of the vehicles and made multiple arrests, but the third vehicle continued, the statement said.
The crash Sunday morning on Highway 85 in Big Wells was the result of a chase that involved Border Patrol agents and Dimmit County deputies.
The sheriff said he didn't know where the immigrants were from but said most migrants who travel through the area are from Central America or Mexico.
The driver and passenger are US citizens and are likely to face state and federal charges, Boyd said.
In total, 12 people were ejected from the SUV when it rolled over during the pursuit.
Some of the wounded were thrown from a vehicle packed with 14 people that was travelling at 100mph (160km/h), County Sheriff Marion Boyd told KFDM News TV. "We've seen this many, many times". Boyd said agents were chasing the SUV when it lost control and overturned. The driver was among those hospitalized, and a deputy who assisted the Border Patrol with the chase found the driver sitting upright in his seat and took him and the passenger into custody.
The sheriff said he didn't know where the immigrants were from.
Four of the migrants reportedly died at the scene, with a fifth later dying at the hospital.
He added: "This is a flawless example of why our borders need to be secure".