Find the Laplace transform $F(s) = {\mathcal L}\left\lbrace f(t) \right\rbrace$ of the function $f(t) = \left(2-t\right)\!\left(h\!\left(t-2\right)-h\!\left(t-5\right)\right)$, for $s \neq 0$.

$\displaystyle F(s) = {\mathcal L}\left\lbrace f(t) \right\rbrace =$ help (formulas)