The Laplace transform of a continuous function over the interval $\displaystyle {\left[{0},\infty\right)}$ is defined by $\displaystyle {F}{\left({s}\right)}={\int_{{0}}^{\infty}}{e}^{{-{s}{x}}}{f{{\left({x}\right)}}}{\left.{d}{x}\right.}$. This definition is used to solve some important initial-value problems in differential equations. The domain of $\displaystyle {F}$ is the set of all real numbers $\displaystyle {s}$ such that the improper integral converges. Find the Laplace transform $\displaystyle {F}$ of the following function:

      $\displaystyle {f{{\left({x}\right)}}}={e}^{{{5}{x}}}$