Answer
$\{(x,y)\in \mathbb{R}^{2}\ \ |\ \ $ $x^{2}+y^{2}\neq 25$ $\}$
Work Step by Step
There are no restricitions on sine, since it is is defined everywhere.
f is defined for points (x,y) that do not yield zero in the denominator.
We exclude all points for which
$x^{2}+y^{2}=25$
This is a circle about the origin of radius $5$.
Since we are excluding it, we graph it with a dashed line.
Domain: all points not lying on circle $x^{2}+y^{2}=25$
or, in set notation, $\{(x,y)\in \mathbb{R}^{2}\ \ |\ \ $ $x^{2}+y^{2}\neq 25$ $\}$
