Obiri who was lining up as the world leader in London produced a devastating burst down the back straight to leave defending champion Almaz Ayana trailing in her wake. "I could see Ayana was not going so I thought, why not?" said Obiri.
Ayana ground the field into submission in the 10,000m on the second day of the championships and she made her intent clear in the 5000m final with a fourth lap of 65.57, followed by 66.21 for the fifth lap. "I am mentally strong so I knew I was capable", said Obiri.
Ayana was unable to burn off Obiri as she had done her rivals in the 10,000m - which she won by over 46sec - with the Kenyan content to let her 25-year-old rival do all the pace-setting.
Ayana, who had won the 10,000m gold in what was her first race of the season, took silver for Ethiopia in 14:40.35 with the Netherlands Sifan Hassan finishing third in 14:42.73.
After a season blighted by a leg injury and illness, Ayana looked back at her imperious best in the 10,000m but it soon became clear these exertions were catching up with the reigning champion. "When I crossed the line I was extremely happy, and just wanted to celebrate".
Muir fourth in the 10,000m earlier this week was left well behind in the 5,000m
"It was a hard race", said Ayana.
"I've had many injuries this year so I am very happy with two medals".
Obiri did not run the 10,000 metres last week and her decision to concentrate on the shorter distance paid off.
Best Australian performance: Dani Stevens smashed the Australian record to finish second behind Croatian Sandra Perkovic in the women's discus final.
Renegade al-Shabab leader defects to government
He left the militant group in 2013 and retreated to his homeland over a disagreement on using foreign fighters in the group. Robow, who was the deputy director of al-Shabab, is the highest official to have ever quit the group.