\begin{align*}

\lim\limits_{x\to 2}\left(4x-3\right)\left(x^2+5\right) & =\left[\left(4\cdot 2\right)-3\right]\left[\left(2\right)^2+5\right]\\

& =\left[8-3\right]\left[4+5\right]\\

& =\left(5\right)\left(9\right)\\

& =45 \ \qquad \ \color{DarkOrange} \left( \text{Answer} \right)\\

\end{align*}