Six patients were taken to San Antonio Military Medical Center in San Antonio, Lt. Edwin Roberts said.
"The Border Patrol was pursuing a vehicle and one of my deputies assisted in the pursuit, and took over the pursuit just west of Big Wells", Mr. Boyd told KSAT-12.
CNN reports they reached out to Yolanda Choates, a spokeswoman for US Customs and Border Protection, but she directed all comments back to the sheriff's department.
Border Patrol officials have repeatedly warned of the dangers of smuggling large numbers of people in vehicles.
Dimmit County Sheriff Marion Boyd says the SUV went out of control at more than 100 miles per hour and overturned on Texas Highway 85, ejecting those inside.
The driver and one passenger are believed to be USA citizens, KABB-TV reports. Border Patrol agents stopped two of the vehicles and made multiple arrests, but the third vehicle continued, the statement said.
Shinnecock Hills beats down some big names at US Open
Poulter followed that with a bogey at the ninth, tumbling from solo second place into a tie for fourth, five shots off the pace. Each entered Friday's second day aiming to improve on first-day frustrations but, in spite of some plus-points, fell short.
Sunday's crash comes amid widespread protests over President Donald Trump's immigration policies that include separating undocumented children from parents caught sneaking them into the country.
Four victims were pronounced dead on the scene and a fifth was pronounced dead after being airlifted to a hospital in San Antonio, Boyd said.
In addition to the driver, one of the passengers, who is also believed to be American, was placed in custody.
Boyd added: "If it can be built, I think it needs to be built. We dealt with him last week", Boyd said.
Images from the scene appeared to show a large four-door SUV-style auto badly wrecked in the middle of the road.
"Our deepest sympathies go out to the families of those who died in the crash", the Border Patrol said.