Consider the following premises. forall y: Q_2(y) <-> P_5(y). P_5(a_5). Can we infer exists y: Q_2(y) from them?
 From P_5(a_5) we can infer exists y: P_5(y). From forall y: Q_2(y) <-> P_5(y) we can infer forall y: P_5(y) -> Q_2(y). Finally, from forall y: P_5(y) -> Q_2(y), exists y: P_5(y) we can infer exists y: Q_2(y). Therefore, the answer is yes.