Answer
$\dfrac{23}{3}$
Work Step by Step
Let us consider that two continuous functions $f(x)$ and $g(x)$ with $f(x)\geq g(x)$ on the interval $[a,b]$ . The area (A) of the region bounded by the graph of $f(x)$ and $g(x)$ on the interval $[a,b]$ can be calculated as: $Area(A)=\int_a^b [f(x)-g(x)] \ dx$
Thus, the area of the region is:
$A=\int_a^b [f(x)-g(x)] \ dx\\ = \int_{0}^{5} [\sqrt {y+4}-(\dfrac{4y}{5}-1)] \ dy \\= [\dfrac{2(y+4)^{3/2}}{3}-\dfrac{4}{5}\dfrac{y^2}{2}+y]_{0}^{5} \\= \dfrac{2}{3}(9^{3/2}) -\dfrac{4}{5}(\dfrac{25}{2})+5-(\dfrac{2(4)^{3/2}}{3})\\=\dfrac{2}{3}(27) -10+5-(\dfrac{2}{3})(8) \\=\dfrac{23}{3}$
