This is a permutation problem
What you should do first is ask how many places are there for the books that the store wants to display. In this case, there are 5 places. Then you ask how many books can you choose from. In this case, 12 books.
So you ask how many books are available for the first place. For the first place, there are 12 books to choose from. After that, how many are left for the second place? There are 11 for the second. Then there are 10 for the third, 9 for the fourth, and 8 for the fifth.
So now you have to multiply all the numbers available for each place together:
12 x 11 x 10 x 9 x 8 = 95040
So there are 95040 different ways to arrange 12 books in five places.