Problem $3$ Additional workspace on the next page

Consider the circuit below. $\backslash ($ v$\_\{$s$\}($t$)=10$ u$($t$)$ V $\backslash ),$ and when $\backslash ($ t$=0^\{-\}\backslash ),$ the initial current flows through the inductor is $1$ A $,$ and the initial voltage across the capacitor is $5$ V $.$

$1)$ Convert the entire circuit from the time domain to the s$-$domain, incorporating the initial conditions, and draw the s$-$domain circuit. $(20$ points$)$

$2)$ Find the Laplace transform of the voltage across the capacitor $\backslash ($ V$($S$)\backslash ).$ Simplify it to the most reduced form. $(15$ points$)$