Can you lose weight if you only eat 500 to 800 calories a day?

You should talk to your doctor before starting a diet, as you want to lose weight but still stay healthy. 500 to 800 calories are very few indeed, so it does not sound OK unless a doctor recommends that specifically to you. Remember that diets need to be balanced too!

In answer to that ^^ I am 5"6 and 112 pounds, And i have not been reccomended by a doctor.

Will i lose weight though?