Answer
$\\(x+5)^2+(y+3)^2=5$
Work Step by Step
RECALL:
The standard form of the equation of a circle with a center of $(h, k)$ and a radius of $r$ units is:
$(x-h)^2 + (y-k)^2 = r^2$
The given circle has its center at $(-5, -3)$ and a radius of $\sqrt3$ units.
Use the standard form above where $h=-5$, $k=-3$, and $r=\sqrt5$ to obtain:
$[x-(-5)]^2 + [y-(-3)]^2 =(\sqrt5)^2
\\(x+5)^2+(y+3)^2=5$