The boat sank in the morning, north of the islands, which China calls the Diaoyus and Japan the Senkakus, Chinese naval sources said.
The dispute over the Japanese-held islets, where Chinese and Japanese ships regularly engage in a cat-and-mouse game, has raised fears of a clash between Asia's biggest powers that could even drag in the US.
The trawler Minxiayu 01003 took on water while it was fishing and sunk. A nearby Chinese naval ship went to the scene and rescued five sailors while another navy ship is helping to look for five who are still missing.
Japan's Coastguard said it had sent an aircraft and a patrol boat to the area to help in the search.