The 33-year-old runner won convincingly in Rio on Saturday with a time of 13 minutes and 31 seconds.
Victory means Farah has now won the 10,000m and 5,000m at two consecutive Olympic Games, having first won the titles at London 2012.
His win helped Team GB surpass London 2012’s medal tally of 65 on day 15 of the Rio Games.
Last Saturday, Farah made history after winning the 10,000m to become the first Britain to win three Olympic golds on the track.
After victory in the 5,000m, his medal tally now stands at four and becomes only the second man to retain both distance titles – dubbed the “double double”.
After finishing the race, Farah said he “couldn’t believe it”, adding “it’s every athlete’s dream”.
Team GB’s medal tally now stands at 66 – 27 gold, 22 silver, and 17 bronze – after 15 days of the Rio Olympics, matching that achieved at London 2012.