Consider the following premises. There is at least one x_5 for which x_5 will read a book. For all x_5, if x_5 reads a book, then x_5 is not bored. For all x_5, x_5 is bored. Can we infer the following from them? There is at least one x_5 for which x_5 will work.
 From the fact that there is at least one x_5 for which x_5 will read a book we can infer that there is at least one x_5 for which x_5 will read a book or x_5 will work. From the fact that for all x_5, if x_5 reads a book, then x_5 is not bored, and that for all x_5, x_5 is bored we can infer that for all x_5, x_5 will not read a book. Finally, from the fact that there is at least one x_5 for which x_5 will read a book or x_5 will work, and that for all x_5, x_5 will not read a book we can infer that there is at least one x_5 for which x_5 will work. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.