Can laser diode be operated with lower than specified voltage?
First, you shouldn't be driving a laser with a fixed voltage, you should be using a constant current source. A fixed voltage source can easily damage a laser diode if the temperature changes and causes the I-V curve to drift up just a little bit. 

Second, if you operate a laser diode below threshold (most likely, 5 V the maximum threshold voltage across all parts and operating conditions, and the actual threshold is somewhat lower) you will get vastly lower optical output. Furthermore, when operating sub-threshold a laser diode will behave more like an LED (much broader optical spectrum) than like a laser.