Cheptegei went 13:07 - 13:03 to set the new 10,000 mark and wipe Kenenisa Bekele from the record books while Gidey, who hadn't won a 5000 race in four years, broke Tirunesh Dibaba's 5000 world record.
It was a special day for distance fans as a 12-year-old women's world record and a 16-year-old men's world record fell in Valencia.
Eight weeks after his 5k WR in Monaco, Joshua Cheptegei will try to break Kenenisa Bekele's 10k mark of 26:17.53 on Wednesday. Shadrack Kipchirchir will try to become just the third American under 27:00, while Letesenbet Gidey wants Tirunesh Dibaba's 14:11.15 5k WR.