Step 1: Determine the total number of books. You have 3 French books, 2 History books, and 5 Math books. Total number of books = $3 + 2 + 5 = 10$ books. Step 2: Calculate the number of arrangements. Since all books are different, arranging them is a permutation of $n$ distinct items. The number of ways to arrange $n$ distinct items is $n!$. In this case, $n=10$. So, the number of ways to arrange the 10 different books is $10!$. Step 3: Calculate the factorial. $$10! = 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1$$ $$10! = 3,628,800$$ The number of ways to arrange the books is: $$\boxed{3,628,800}$$