Prove assertion that $\backslash$sqrt$[3]\{$n$^3-5$n$\}\backslash$in $\{\backslash$rm $\backslash$Omega$\}\backslash$left$($n$\backslash$right$)$ is true by definition. Clearly provide and demarcate the following elements in your proof:

Give a formal definition of the asymptotic notation that includes the relevant inequality. $[4$ points$]$

State what the function f$($n$)$ and g$($n$)$ in the definition are with respect to the claim. $[4$ points$]$

State the goals of the proof; that is$,$ state what you would like to find$/$show $-$ the relevant multiplicative constant$($s$)$ and integer constant for which the inequality in the definition is true in some positive infinite interval. $[4$ points$]$

Provide detailed algebraic manipulation and mathematical arguments to derive the constants. $[10$ points$]$

Give concluding remarks that include how the constants that you derive make the inequality in the definition hold and the proposition true. $[3$ points$]$