Answer
$1287$
Work Step by Step
We know that if we want to select $r$ objects out of $n$ disregarding the order, we can do this in $_nC_r=\frac{n!}{(n-r)!r!}$ ways.
Hence here the number of possibilities: $_{13}P_5=\frac{13!}{(13-5)!5!}=1287$