My husband got physical custody of his son in the divorce. My step-son has not spoken to his biological mother in over 5 years. He wants me to adpot him. (Which I am all for!). My question is what if the biological mother won't agree to it, can we still get it done?

It may or may not be legal to adopt an adult in your state. The parents of the child don't have a say if the child is of legal age and full mental capacity.