Let $K$ be the measure of the area bounded by the $x$-axis, the line $x=8$, and the curve defined by
\[f={(x,y)\quad |\quad y=x \text{  when  } 0 \le x \le 5, y=2x-5 \text{  when  } 5 \le x \le 8}.\]
Then $K$ is:
$\text{(A) } 21.5\quad \text{(B) } 36.4\quad \text{(C) } 36.5\quad \text{(D) } 44\quad \text{(E) less than 44 but arbitrarily close to it}$
The shape can be divided into a triangle and a trapezoid.  For the triangle, the base is $5$ and the height is $5$, so the area is $\frac{5 \cdot 5}{2} = \frac{25}{2}$.  For the trapezoid, the two bases are $5$ and $11$ and the height is $3$, so the area is $\frac{3(5+11)}{2} = 24$.  Thus, the total area is $\frac{25}{2} + 24 = \frac{73}{2} = \boxed{\textbf{(C) } 36.5}$.