Klosterhalfen, who led the race from the gun, clocked an impressive 14:26.76 to break 20-year-old Irina Mikitenko's German record of 14:42.03.
"I wanted to run as fast as I can:" Klosterhalfen told ARD sports.
The 22-year-old Klosterhalfen lapped every runner in the race except Alina Reh, who took silver at with 15:19.42.
Klosterhalfen moves to fourth on the European all-time list ahead of Great Britain’s Paula Radcliffe.
Splits:
1km 2:54.88
2km 5:49.45
3km 8:44.49
4km 11:37.65
See full women's 5000m results here
Streaming and other event info here.
Watch Race Video