## Calculus (3rd Edition)

$3x+4y-z=0.$
Since the plane is parallel to $3x+4y-z=5$, then its normal vector will be $\langle 3,4,-1\rangle$, and since the plane passes through the origin, the equation of the plane is given by $$3(x-0)+4(y-0)-(z-0)=0\Longrightarrow 3x+4y-z=0.$$