The impact of the accident was so fierce that the elephants - one male, three female and the calves - were dragged along for about a kilometre before the train finally came to a halt.
The train was delayed for almost seven hours at the site and moved on after the tracks were cleared.
Forest officials blamed railway authorities for the accident. "We had informed them in advance that elephants might cross the track around midnight. Timely action could have averted the accident," Odisha's principal chief conservator of forest JD Sharma said.
Railway officials, however, said they received no such early alert. "We received the information exactly at the same time when the accident occurred. Had the forest department given the information a bit earlier, the situation would have been different," said east coast railway's chief public relation officer RN Mohapatra.
Odisha forest and environment minister Bijayshree Routray said the state government would take up the matter with the railway ministry.
In August, a train had run over an elephant in the same area, and two more were similarly killed in western Odisha's Keonjhar district.