There are two 'C' ratings of lipo batteries. There is a constant discharge and a peak (or burst) discharge.
For example, this 5000mAh, 5S battery has a Constant Discharge of 30C and a peak discharge of 40C for 10 seconds. Therefore, the maximum constant current is 150A (30C x 5Ah) and the maximum burst current is 200A (40C x 5Ah).