Answer
The equation has no real solutions. Hence, it has no points.
Work Step by Step
Write
${x^2} - 4x + {y^2} + 5 = 0$
${x^2} - 4x + 4 - 4 + {y^2} + 5 = 0$
${\left( {x - 2} \right)^2} - 4 + {y^2} + 5 = 0$
${\left( {x - 2} \right)^2} + {y^2} = - 1$
Notice that the left-hand side is nonnegative because it is the sum of two squares. But the right-hand side is negative, so there is no real solutions. Hence, it has no points.