If the point (-5, -12) is a point on the terminal side of an angle in standard position, how do you find the radius of the circle?

The line $A O$ is the radius.
You can use Pitagora's Theorem applied to the triangle $A B O$ giving:
$A O = \sqrt{{\left(- 5\right)}^{2} + {\left(- 12\right)}^{2}} = 13$
Using trigonometry (in particular inverse trigonometric functions) you can also find the angle that the radius $A O$ makes with the positive $x$ semi-axis!