My particular KL5 runs in regulation with an input voltage range between 3.2V to 7.3V. So Klaus is correct it should run off 3 or 4 NiMH cells, and even five maybe six if they're not fresh off the charger. This is based on data that I took and posted here:
KL5 Input Voltage vs Current
Note that at around 7.3V, the LED is going into direct drive mode and if you continue increasing the voltage, the current goes up substantially. At this point, you're following the I-V curve in the LED data sheet. You risk damaging the circuit but not the LED, if you go well above an amp at the input once you exceed Vf.
CM