If my mom is 5'5 and my dad is 5'6 what will be my permanent height ? im 5'1 now at 17 but im not sure if my bone plates are closed yet

No way to tell: A bone age x-ray may give your pediatrician some information about any remaining potential growth.

Probably 5'1": The height expected from any female offspring is the average of both parents less 2.5 inches, give or take an inch. At 5'1" and 17 you may have a little growth left, but I wouldn't expect much. If you have not grown more than a half inch in the past year You are done or close to it.