Consider the following premises. ~Q_5(a). forall x_5: P_5(x_5) or ~Q_5(x_5). forall x_5: P_5(x_5) -> Q_5(x_5). Can we infer ~P_5(a) from them?
 From forall x_5: P_5(x_5) or ~Q_5(x_5) we can infer forall x_5: Q_5(x_5) -> P_5(x_5). From forall x_5: Q_5(x_5) -> P_5(x_5), forall x_5: P_5(x_5) -> Q_5(x_5) we can infer forall x_5: Q_5(x_5) <-> P_5(x_5). From forall x_5: Q_5(x_5) <-> P_5(x_5) we can infer Q_5(a) <-> P_5(a). Finally, from Q_5(a) <-> P_5(a), ~Q_5(a) we can infer ~P_5(a). Therefore, the answer is yes.