Answer
$${\text{The equation does not represent a graph}}$$
Work Step by Step
$$\eqalign{
& {\left( {x + 7} \right)^2} + {\left( {y - 5} \right)^2} + 4 = 0 \cr
& {\text{Subtract 4 from each side of the equation}} \cr
& {\left( {x + 7} \right)^2} + {\left( {y - 5} \right)^2} + 4 - 4 = - 4 \cr
& {\left( {x + 7} \right)^2} + {\left( {y - 5} \right)^2} = - 4 \cr
& {\text{The equation is in the form }}{\left( {x - h} \right)^2} + {\left( {y - k} \right)^2} = {r^2} \cr
& {\text{We can note that }}{r^2}{\text{ is negative, }} \cr
& {\text{then the equation does not represent a graph}} \cr} $$
