Consider the following premises. For all x_5, if x_5 were a poet, then x_5 is playing tennis. For all x_5, x_5 is a scientist if and only if x_5 will play tennis. For all x_5, x_5 is a poet. Can we infer the following from them? For all x_5, x_5 is a scientist if and only if x_5 will play tennis.
That is one of the premises. Therefore, the answer is yes.