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You can simplify the problem by considering it as two different problems. The first involves consider the five-book chunk as a single book, and calculating the permutations there. The second involves the permutations of the books within the five-book block. Multiplying these together gives you the total permutations.

Permutations of five objects is 5!, five gives 5!, so the total permutations are:

5!5! = 5*5*4*4*3*3*2*2 = 263252 = 14,400 permutations

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Q: How many ways can 9 books be arranged on a shelf so that 5 of the books are always together?
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