Definition $-$ Laplace Transform

Let $f$ be a function defined on $[0,).$ Then the function $F$ defined by

$F(s)={\displaystyle \underset{0}{\overset{}{}}}{e}^{-st}f(t)dt$

is said to be the Laplace transform of $f.$ The domain of $F(s)$ is the set of values of $s$ for which the given improper integral converges.

Use the definition of a Laplace transform to find $L\{f(t)\}.($Write your answer as a function of $s.)$

$f(t)=t{e}^{5t}$