I have a 1W 445nm LASER diode. It's rated for 4.3 to 4.6V and pulls around 1A of current
LASER drivers are "tricky". They use feedback from a "3rd pin" on the LASER diode to measure the light-output. The "5V" driver might work if the feedback & power setting is correct because it will automatically-continuously adjust the voltage & current for the right amount of power (voltage & current). The safest thing is to buy a laser module with a built-in driver, or get the recommended driver from the LASER manufacturer/supplier. That's especially true if the LASER needs to be pulsed or modulated because most drivers are designed for continuous output. Here is a web page all about LASERS & drivers.Hmmm.... Power is Voltage x Current, so that would be around 4.5 Watts.
How about telling us which laser diode?