Consider the following premises. w or ~q. ~p_5. p_5 <-> q. w -> q. Can we infer ~w from them?
 From w or ~q we can infer q -> w. From p_5 <-> q, ~p_5 we can infer ~q. From w -> q, q -> w we can infer w <-> q. Finally, from w <-> q, ~q we can infer ~w. Therefore, the answer is yes.