The SUV lost control at over 100mph and overturned on Texas Highway 85, about 90 miles (145km) north of the Mexican border, Dimmit County Sheriff Marion Boyd said.
Some of the injured were ejected from the Chevy Suburban vehicle.
From what we can tell the vehicle ran off the road and caught gravel, and then tried to re-correct and then caused the vehicle to turn over several times, Mr Boyd told CNN.
We’ve seen this many, many times, in not only this county but other counties along the border. This is a perfect example of why our borders need to be secure.
Four people were pronounced dead at the scene while a fifth died at a hospital.
Most of the occupants were believed to be living in the US without legal permission.
Mr Boyd said the driver and one passenger were believed to be US citizens. Both are in custody.
Some of the injured people were taken by helicopter to San Antonio, about 90 miles northeast.
The crash comes amid heightened tensions over the treatment of immigrants at the southern border.
The Trump administration has said tougher immigration policies are needed to deter immigrants from entering America illegally.
News Source SkyNews