Answer
$2,598,960$ ways.
Work Step by Step
The order in which the cards are select does not matter and no card can be selected more than once.
It is a combination of 52 distinct cards taken 5 at a time:
$_{52}C_5=\frac{52!}{5!(52-5)!}=\frac{52!}{5!\times47!}$
But, $52!=52\times51\times50\times49\times48\times(47\times46\times45\times...\times3\times2\times1)=52\times51\times50\times49\times48\times47!$
$_{52}C_5=\frac{52\times51\times50\times49\times48\times47!}{5!\times47!}=\frac{52\times51\times50\times49\times48}{5\times4\times3\times2\times1}=2,598,960$
