By using the properties of definite integrals,evaluate the integral $\int_{-5}^{5}|x+2| d x$.

Let $I = \int_{-5}^{5}|x+2| d x$.
It can be seen that $(x+2) \leq 0$ on $[-5, -2]$ and $(x+2) \geq 0$ on $[-2, 5]$.
Using the property $\int_{a}^{b} f(x) d x = \int_{a}^{c} f(x) d x + \int_{c}^{b} f(x) d x$,we have:
$I = \int_{-5}^{-2} -(x+2) d x + \int_{-2}^{5} (x+2) d x$
$I = -\left[\frac{x^{2}}{2} + 2x\right]_{-5}^{-2} + \left[\frac{x^{2}}{2} + 2x\right]_{-2}^{5}$
$I = -\left[\left(\frac{(-2)^{2}}{2} + 2(-2)\right) - \left(\frac{(-5)^{2}}{2} + 2(-5)\right)\right] + \left[\left(\frac{5^{2}}{2} + 2(5)\right) - \left(\frac{(-2)^{2}}{2} + 2(-2)\right)\right]$
$I = -\left[(2 - 4) - (12.5 - 10)\right] + \left[(12.5 + 10) - (2 - 4)\right]$
$I = -[-2 - 2.5] + [22.5 - (-2)]$
$I = -[-4.5] + [24.5]$
$I = 4.5 + 24.5 = 29$.