Answer
False.
Work Step by Step
$x=2y-y^2+5=-(y-1)^2+6\\x-6=-(y-1)^2$
If the major axis of the parabola is parallel to the x-axis then it is in the form of $k(x-a)=(y-b)^2$, where $(a,b)$ is the vertex of the parabola and $k$ is a constant. (positive if open right, negative if open left).
Thus it is open to the left.
