Macbook 5,2 Black Screen Issue
A couple of things to try would be:
Reset the PRAM

Restart your Mac

As soon as you press the power button to turn it back on, hold the
⌘ +  ⌥ + P + R keys until you hear the startup chime twice


Reset the SMC

Shut down your Mac

Remove the battery and unplug the power cable

Hold down the power button for 10 seconds and then let go

Restart your Mac normally


These steps may not resolve your issue, but it's worth a shot. If they do no resolve the issue, it is likely related to the inverter board, which sends power to your display backlight. It's relatively common in this model MacBook.
It shouldn't be to expensive to repair, but I would not recommend doing it yourself. It's taken me hours to do that repair, and that's in an Apple Store with all the right tools, Apple Technician Guides and the proper training.