The perpendicular distance from the point $\left(2,-7\right)$  to the line $2x-5y-10=0$  is

$2x-5y-10=0$

The perpendicular distance from $\left(2,-7\right)$  to the line $2x-5y-10=0$  is

$=\left|\frac{a{x}_1+b{y}_1+c}{\sqrt{a^2-b^2}}\right|$

$=\left|\frac{2\left(2\right)-5\left(-7\right)-10}{\sqrt{2^2+{\left(-5\right)}^2}}\right|$

$=\left|\frac{4+35-10}{\sqrt{4+25}}\right|$

$=\left|\frac{29}{\sqrt{29}}\right|$

$=\sqrt{29}units$