The distance of a point $\left(x_{1}, y_{1}, z_{1}\right)$ from the plane $a x+b y+c z+d=0$ is given by
$=\left|\frac{a x_{1}+b y_{1}+c z_{1}+d}{\sqrt{a^{2}+b^{2}+c^{2}}}\right|$
$\therefore $ Distance of the point $(2,1,0)$ from the plane $2 x+y+2 z+5=0$ is equal to
$=\left|\frac{2 \times 2+1 \times 1+2 \times 0+5}{\sqrt{(2)^{2}+(1)^{2}+(2)^{2}}}\right|=\left|\frac{4+1+5}{\sqrt{4+1+4}}\right|=\frac{10}{3}$