#### Answer

$z=-15$

#### Work Step by Step

Multiplying both sides of the given equation, $
\dfrac{10}{z}=\dfrac{5}{z}-\dfrac{1}{3}
,$ by the $LCD=
3z
$, then,
\begin{array}{l}\require{cancel}
3z\left( \dfrac{10}{z} \right)=\left( \dfrac{5}{z}-\dfrac{1}{3} \right)(3z)
\\\\
3(10)=5(3)-1(z)
\\\\
30=15-z
\\\\
z=15-30
\\\\
z=-15
.\end{array}