Does it use more energy to shut my computer down or leave it in sleep mode. I have a Mac desktop G-5?

Sleep mode uses more power. Turn your computer off. It's what I do.

It is a no brain question of course it uses less energy to shut it down than to put it in to sleep mode, because it is still partially running.

Yes it does, the only way to save energy is to switch it off. All electronic equipment left in stand by can use up to 1 watt per hour.

When its not in use, unplug it. Even if its not on, its still using energy for the led lights and other things. I try to unplug everything when I dont use it. It saves a lot of money on the power bill.

sleep mode uses more energy. shuting it down wont take much

leaving it in sleep mode is like keeping it on auto, but not using power. It takes more energy to restart the whole connection process.