DIAGNOSIS The tool is getting power to the electronics (hence the light), but the motor isn't engaging. This is almost always a worn-out or failed trigger switch.
FIX Yeah, this one's common. You'll need to replace the switch assembly. Unplug the battery. Remove the two screws on the top of the handle (under the rubber grip) and the screw inside the battery port. Carefully separate the clamshell housing. You'll see the trigger switch wired into the main assembly. Take a clear photo of the wiring connections before you disconnect anything. The replacement part is Makita part number 413038-6 (switch assy). Swap it over, reassemble, and you should be back in business.
IF THAT DIDN'T WORK If a new switch doesn't fix it, the issue could be the motor brushes. On this brushless model (XRJ05Z), the motor is sealed, but there are still carbon brushes that contact the armature. If they're worn to nothing or stuck, the motor won't run. This requires more disassembly to inspect the brush holders at the rear of the motor.
HEADS UP When you're reassembling the clamshell, make sure the rubber seal around the trigger is seated properly. If it's pinched or out of place, you'll get sawdust and debris inside the electronics, which will cause more problems down the line.