Answer
$\dfrac{25}{2}$
Work Step by Step
We can see from the sketch that the area we want to evaluate is equal to the area of a right triangle with $b = 5$ and $h = 5$, therefore $\int_{0}^{5} (5-|x-5|) \ dx = \dfrac{5 \times 5}{2} = \dfrac{25}{2}$ which is the area of a triangle (base $b$ times height $h$ divided by 2).
