The Houston Police Department said the five suspects used a pickup truck to smash through the pharmacy's front door at about 4 a.m. on Irvington Boulevard near Cavalcade Street.
Officers said they were unsure whether anything was stolen inside that store.
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Authorities said they believe the group might have also tried to steal another ATM at a Chase Bank about 30 minutes earlier, but police said they did not find anything at that scene.
The group was arrested after leading police on a chase, according to police, who said they had to use a pit maneuver to stop them.
A total of five suspects, one adult and four juveniles, are now in custody, HPD said.