## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

$6,302,555,018,760$ 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: $P(365,5) \\= 365\times364\times363\times362\times361 \\= 6,302,555,018,760$