Consider the following premises. For all x_5, x_5 is a politician. For all x_5, x_5 is a politician if and only if x_5 will make tea. There is at least one x_5 for which if x_5 plays tennis, then x_5 is making tea. Can we infer the following from them? There is at least one x_5 for which x_5 will make tea.
 From the fact that for all x_5, x_5 is a politician if and only if x_5 will make tea we can infer that for all x_5, if x_5 were a politician, then x_5 is making tea. From the fact that for all x_5, x_5 is a politician we can infer that for all x_5, x_5 is a politician or x_5 will play tennis. Finally, from the fact that for all x_5, if x_5 were a politician, then x_5 is making tea, that there is at least one x_5 for which if x_5 plays tennis, then x_5 is making tea, and that for all x_5, x_5 is a politician or x_5 will play tennis we can infer that there is at least one x_5 for which x_5 will make tea. Therefore, the answer is yes.