During the chase, the driver of the 2007 Suburban, 20-year-old Jorge Luis Monsivais Jr. of Eagle Pass, Texas, crashed his SUV as he entered the town of Big Wells, Texas.
Four victims were dead at the scene, Boyd said.
One of the four taken to the San Antonio hospital later died, the department said. Officials have not released the names of the driver or any of the 13 passengers.
Most of the occupants in the SUV were believed in the country without legal permission.
Boyd credited "good police work" for the reason why deputies started pursuing the vehicle.
In a later interview, Boyd said the auto reached 100 miles per hour before the driver lost control and crashed. Multiple arrests were made from both vehicles.
Led coalition hits Syrian army post, causing casualties
The US-led coalition is supporting an alliance of Syrian Arab and Kurdish militia fighting Islamic State northeast of Albu Kamal. Asked about the reported air strikes, an Israeli military spokeswoman said: "We do not comment on foreign reports".
Dimmit County Sheriff Marion Boyd says the driver wasn't seriously injured, so he was taken straight into Homeland Security custody, where he is being investigated. "He's talking", Boyd said. "We've seen this many many times, not only in this county but in other counties along the border".
He added: 'This is a flawless example of why our borders need to be secure.
"Not just a wall alone, there needs to be sensors, there needs to be cameras, there needs to be personnel to man it", Body said. There needs to be sensors'.
The U.S. leader, in a Twitter comment, again defended the border policy leading to the separation of children from their parents.
The recording gives an apparent insight into the conditions on the southern U.S. border, where migrant families are split up and young children are being kept in cages in camps as part of a controversial clampdown on immigration introduced by Donald Trump's administration. "If a parent left a child in a cage with no supervision with other 5-year-olds, they'd be held accountable". The Border Patrol's Rio Grande Valley office is now charging more than a 1,000 adults each week with illegal entry, a misdemeanor.
That outlook is shared by Attorney General Jeff Sessions and the president. Massachusetts Gov. Charlie Baker, a Republican, reversed a decision to send a National Guard helicopter from his state to the Mexican border to assist in a deployment, citing the administration's "cruel and inhumane" policy. Additionally, Jose Rodriguez, a local lawmaker, further describes the United States plan as "totally inhumane" and "outrageous", adding that "it should be condemned by anyone who has a moral sense of responsibility".