Answer
\[\cos5x+i(-\sin 5x)\]
Work Step by Step
We will use the Euler's formula
\[e^{i\theta}=\cos \theta+i\sin\theta\]
We can write $\;e^{-5ix}=e^{i(-5x)}$
By using Euler's formula
$e^{-5ix}=\cos(-5x)+i\sin (-5x)$
$e^{-5ix}= \cos5x+i(-\sin 5x)$
Here $\;u(x)=\cos 5x $ and $\;v(x)=-\sin 5x$
Hence ,
$e^{-5ix}= \cos5x+i(-\sin 5x)$.
