Answer
$e^{5x}$
Work Step by Step
Use hyperbolic function formula as follows: $ \cosh x= \dfrac{e^x+e^{-x}}{2}$ and $ \sinh x= \dfrac{e^x-e^{-x}}{2}$
Need to solve: $\cosh (5x) + \sinh (5x)$
This implies, $\cosh (5x) + \sinh (5x)=\dfrac{e^{5x}+e^{-5x}}{2}+\dfrac{e^{5x}-e^{-5x}}{2}$
Hence, $\cosh (5x) + \sinh (5x)=e^{5x}$
