Per week, one cow produces 108 liters / 6 cows = <<108/6=18>>18 liters/cow.
The cows produced 2160 liters of milk over 5 weeks. So we have 2160 liters / 18 liters/cow = <<2160/18=120>>120 cows.
Further, we have to divide 120 cows / 5 weeks = <<120/5=24>>24 cows.
#### 24