Answer
$6x-22y-29z=-101$
Work Step by Step
The plane passes through the points $(0,-2,5)$ and $(-1,3,1)$ and is perpendicular to the plane $ 2z=5x
+4y$.
Normal vector is: $\lt 5,4,-2\gt $
Points are $P=(0,-2,5)$ and $Q=(-1,3,1)$ and
Thus, $PQ\times N=\lt 6,-22, -29\gt$
The general form of the equation of the plane is:
$a(x-x_0)+b(y-y_0)+c(z-z_0)=0$
or, $ax+by+cz=ax_0+by_0+cz_0$
Plugging in the values $\lt 6,-22, -29\gt$, we get
$6x-22(y+2)-29(z-5)=0$
After simplification, we get
$6x-22y-29z+101=0$
or, $6x-22y-29z=-101$