Chapter 12 - Counting and Probability - Section 12.2 Permutations and Combinations - 12.2 Assess Your Understanding - Page 875: 48

$ 6,302,555,018,760$ ways

This is a permutation (because order matters) where repetition is not allowed. We have $n = 365, \text{ and } r = 5$. Using the formula $P(n, r)=\dfrac{n!}{(n-r)}!$ gives: $P(365,5) \\= 365\times364\times363\times362\times361 \\= 6,302,555,018,760$