The 33-year-old finished in 13 minutes 3.30 seconds to beat Hagos Gebrhiwet of Ethiopia by just over a second here on Saturday, reports Xinhua.
Bernard Lagat of the United States took bronze, clocking his best timing of the season at 13:06.78.
Farah is only the second man to win the 5,000m and 10,000m at the same Games after Finland's Lasse Viren, who achieved the feat in 1972 and 1976.
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