The 614-ton fishing boat with 42 sailors aboard sank about 4:30 a.m. South Korean time (1930 GMT), some 1,400 miles (2,250 kilometers) south of New Zealand, South Korea's Foreign Ministry and coast guard said.
Maritime New Zealand said 20 survivors were recovered from the South Korean owned and operated No.1 In Sung fishing boat. South Korean and New Zealand fishing vessels were looking for the missing sailors.
On board the sunken vessel were eight South Koreans, eight Chinese, 11 Indonesians, 11 Vietnamese, three Filipinos and one Russian, South Korea's Foreign Ministry said in a statement.
The dead included two Indonesians, two South Koreans and one Vietnamese, a ministry official said, speaking on condition of anonymity because of office rules.
New Zealand's search and rescue coordination center said the 20 survivors and five dead fishermen were on board the South Korean fishing vessel No. 707 Hongjin. Survival times in the water in the area would likely be about 10 minutes without lifejackets or immersion suits, the center said in a statement.
South Korean media outlets reported that high waves in the area were hampering the rescue operation.
Officials at the South Korean-based company that owns the boat had no immediate comment.
Associated Press writer Ray Lilley in Wellington, New Zealand, contributed to this report.