Answer
Level surfaces are of the form
$x^{2}+3y^{2}+5z^{2}=k^{2}$
(we chose $k^{2}$ on the RHS because the sum on the left side can't be negative.)
When $k\neq 0, $ a family of circular cylinders with x as the axis, radius k.
When $k=0,$ the x-axis.
Work Step by Step
(Graphed with geogebra.)