Custody Rights for my nephew?

Your parents need to file for legal guardianship and/or custody. Given that his mother abandoned him and they have been his sole providers & caregivers for the first 5 years of his life means they have a good chance of gaining custody. Don't be surprised if the mother is granted visitation (or even custody) if her life has turned around & she can prove she can provide for him now though. If the courts award custody to her, be sure you and your parents have visitation privileges written into the order to keep her from just taking off with him.