The Coast Guard said Thursday that it had found four additional bodies in its search for dozens of migrants lost at sea off Florida but that it would call off its active search for survivors at sunset if it doesn’t receive any new information.

Authorities have now found a total of five bodies, leaving 34 missing. They have stressed the difficulty of finding survivors in the turbulent waters of the Gulf Stream.

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A man who was found clinging to the hull of the overturned 25-foot (7-meter) boat on Tuesday about 40 miles (64 kilometers) off Fort Pierce, Florida, said the boat capsized late Saturday after he and 39 others had set out for Florida from Bimini, a chain of islands in the Bahamas about 55 miles (88 kilometers) east of Miami.

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“We don’t think it is likely that anyone else has survived,” Coast Guard Capt. Jo-Ann F. Burdian told a news conference.

Authorities said the overturned boat was about 100 miles (160 kilometers) north of where it capsized. No one was wearing a life jacket, the rescued man told authorities.