Boyd said a Dimmitt County Sheriff's deputy took over the chase just west of Big Wells, but the vehicle, which was traveling around 100 miles per hour, ran off the road onto the gravel before flipping several times when it tried to get back on the roadway, the sheriff said.
"We've seen this many, many times, in not only this county but other counties along the border", Boyd told CNN.
Four people believed to be undocumented immigrants were pronounced dead on the scene with a fifth pronounced dead after being transported to a San Antonio hospital.
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Launching ballistic missiles towards densely populated cities and villages breaches the global humanitarian law, he added. Some 70 per cent of Yemen's food enters via the port, as well as the bulk of humanitarian aid and fuel supplies.
Dimmit County Sheriff Marion Boyd told the outlet another five passengers were rushed to San Antonio Military Medical Center for emergency care.
"It's just extremely busy, we need the assets down here, we have a problem", Boyd said.
5 immigrants killed in rollover crash in Dimmit, Texas. He said at least one and possibly two others died at a hospital.
Border Patrol officials have repeatedly warned of the dangers of smuggling large numbers of people in vehicles.
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He added: "This is a ideal example of why our borders need to be secure".
The sheriff said he hadn't spoken to Border Patrol on the exact cause of the pursuit and nature of the crash.
Authorities are investigating the scene where a vehicle full of undocumented immigrants being chased by Border Patrol agents crashed.
Representatives for both U.S. Customs and Border Protection and the Dimmit County Sheriff's Office did not immediately respond to HuffPost's request for comment.
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Actor Sylvester Stallone arrives at the 88th Academy Awards nominees luncheon in Beverly Hills, California , February 8, 2016. The #MeToo campaign took off a year ago following sexual assault allegations against Hollywood mogul Harvey Weinstein .