Answer
See below
Work Step by Step
From geometry, a line tangent to a circle is perpendicular to the radius at the point of tangency. The radius with endpoint $(-5,3)$ has slope $m=\frac{0-3}{0+5}=-\frac{3}{5}$, so the slope of the tangent line at $(-5, 3)$ is the negative reciprocal of $\frac{-3}{5}$. An equation of the tangent line is as follows:
$$y-3=\frac{5}{3}(x+5)\\y=\frac{5}{3}x+\frac{34}{3}$$
