Consider the following premises. ~q. q_5 -> q. q <-> q_5. Can we infer q_5 from them?
 From q <-> q_5 we can infer q -> q_5. From q -> q_5, q_5 -> q we can infer q <-> q_5. Finally, from q <-> q_5, ~q we can infer ~q_5, which contradicts q_5. Therefore, the answer is no.