What is the inverse $Z$-transform for $X(z) = \frac{5z}{3z-15}$?

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I have been trying to figure out this for quite some time but my basic mathematical understanding does not want to co-operate.

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Hint. One may write $$ X(z)=\frac53 \cdot \frac{1}{1-5\cdot z^{-1}} $$ then using the linearity of the $Z$-transform and using a table of common $Z$-transform pairs gives $$ \frac53 \cdot5^n \: u[n] $$ as being the signal, where $$ u : n \mapsto u[n] = \begin{cases} 1, & n \ge 0 \\ 0, & n < 0 \end{cases} $$ is the Heaviside step function.