Twenty survivors were rescued shortly after the 614-ton vessel went down some 1,400 miles south of New Zealand, South Korea's Foreign Ministry and coast guard said.
Any others in the water would be dead in 10 minutes without special suits or lifejackets, though nearby fishing boats launched a frantic search in hopes that some may have made it into a life raft, New Zealand's search and rescue center said.
"We were fortunate that there were a number of vessels in the general area (where the boat sank), so they were able to provide assistance," said Ross Henderson, a spokesman for the center. "Obviously, now, we're trying to determine the status of those 17 missing as quickly as possible."
Fishing boats from New Zealand and South Korea had joined the search, according to Maritime New Zealand.
As hours passed, South Korean coast guard officer Ji Kwan-tae said it was difficult to expect the missing sailors to be alive because of the ocean's freezing temperature. Ji said he had no information on whether the missing sailors were wearing lifejackets or aboard lifeboats.
The South Korean owned and operated No.1 In Sung fishing boat had 42 on board when it sunk: eight South Koreans, eight Chinese, 11 Indonesians, 11 Vietnamese, three Filipinos and one Russian, South Korea's Foreign Ministry said in a statement.
The confirmed dead included two Indonesians, two South Koreans and one Vietnamese, a ministry official said, speaking on condition of anonymity because of office rules.
The Chinese Embassy in South Korea said four Chinese sailors were missing while four others were rescued, China's official Xinhua News Agency reported told Xinhua.
New Zealand's search and rescue coordination center said the 20 survivors and bodies of the five dead were on board the South Korean fishing vessel No. 707 Hongjin.
Officials hoped missing crew members were able to get into a life raft or had some other survival equipment, Henderson told New Zealand's National Radio.
"Given the conditions, we're searching as quickly as we can" to locate the missing fishermen, he said.
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.
It was unclear why the vessel sank in light winds and a relatively mild 3-foot swell.
Separately, South Korean media outlets reported that high waves that later developed in the area were hampering the rescue operation.
Officials at the South Korean-based company that owns the boat had no immediate comment.