A new hard drive is usually not enough to trigger Windows' re-activation. Try cloning the old drive to the new drive (most cloning software is smart enough to shrink partitions when the destination drive is smaller). You will need a desktop or an external enclosure to do this since the computer needs to access both drives at once. Be sure to clone the entire drive, not just the Windows partition. Acronis is the most common pay cloning software. As for free software, EaseUS and Clonezilla seem to be the most frequently recommended.
Once it's cloned, put the 500GB drive into the laptop and try booting. If it works, then you're done. If it asks for re-activation, then you can decide if you want to re-activate or reinstall.