Answer
Paraboloid
Work Step by Step
We can re-write the equation as follows:
$x=y^2+z^2-2y-4z+5$
$\implies x=(y^2-2y)+(z^2-4z)+5$
$\implies x=(y^2-2y+1)+(z^2-4z+4)+5-1-4$
$\implies x=(y-1)^2+(z-2)^2$
We see that this is a paraboloid whose vertex is: $(0,1,2)$. It opens in the +x-axis direction.