Simple ?

Calculus Level 4

Given that

${ I }(n)=\int _{ 0 }^{ \frac { \pi }{ 4 } }{ \cos ^{ n }{ x } \, dx },$

if $I(5) = \frac { a\sqrt { b } }{ c }$ , what is $a + b + c?$

Details and Assumptions:

You can use $\int { \cos { ax } } \, dx =\frac { 1 }{ a } \sin { ax }$ .
$a, b, c$ are positive integers, $\gcd(a,c)=1,$ and $b$ is a square-free integer.