Ans: (C)
Hint : \(\int_{0}^{5} \max \left\{x^{2}, 6 x-8\right\} d x\)
$$
\text { Let } \begin{aligned}
f(x) &=x^{2}-6 x+8 \\
&=(x-4)(x-2)
\end{aligned}
$$
(1)
$$
\begin{aligned}
&\therefore \text { For } x \in[0,2] \cup[4,5], f(x)>0 \text { and in } x \in[2,4], f(x)<0 \\
&\int_{0}^{5} \max \left(x^{2}, 6 x-8\right)=\int_{0}^{2} x^{2} d x+\int_{2}^{4}(6 x-8) d x+\int_{4}^{5} x^{2} d x=\frac{8}{3}+20+\frac{61}{3}=43
\end{aligned}
$$
