Consider the following premises. For all x_5, x_5 will listen to a song. There is at least one x_5 for which if x_5 were a scientist, then x_5 is a soldier. For all x_5, x_5 is a soldier if and only if x_5 will listen to a song. Can we infer the following from them? There is at least one x_5 for which x_5 is a soldier.
 From the fact that for all x_5, x_5 will listen to a song we can infer that for all x_5, x_5 will listen to a song or x_5 is a scientist. From the fact that for all x_5, x_5 is a soldier if and only if x_5 will listen to a song we can infer that for all x_5, if x_5 listens to a song, then x_5 is a soldier. Finally, from the fact that for all x_5, if x_5 listens to a song, then x_5 is a soldier, that there is at least one x_5 for which if x_5 were a scientist, then x_5 is a soldier, and that for all x_5, x_5 will listen to a song or x_5 is a scientist we can infer that there is at least one x_5 for which x_5 is a soldier. Therefore, the answer is yes.