The chartered jet operated by LaMia was carrying Chapecoense, a soccer team which plays in Brazil's top division.
It crashed at around 10 p.m. ET on Monday while on its way from Santa Cruz in Bolivia to Medellin's international airport, which is located at an elevation of 7,000 feet.
Alfredo Bocanegra, the head of Colombia's civil aviation agency, said that communication with Bolivian aviation officials suggested the plane was experiencing electrical problems. However, he added that investigators would have to evaluate reported testimony from a female flight attendant who said the plane had run out of fuel.
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Authorities said the five survivors included soccer player Alan Ruschel, flight attendant Ximena Suarez and aircraft mechanic Erwin Tumiri.
A doctor who appeared on Colombian TV said that Ruschel was being operated on after suffering multiple injuries to his limbs and a lumbar spine fracture. The 27-year-old defender was in an intensive care unit.
Suarez was listed in stable condition while Tumiri suffered non-life threatening injuries, hospital officials said.
Chapecoense had been scheduled to play the first of a two-game Copa Sudamericana final against Medellin-based Atlético Nacional on Wednesday..