  We study the constraints on the anomalous coupling $g^Z_5$ that can be
obtained from the analysis of the reaction $\gamma\gamma \rightarrow W^+ W^- Z$
at future linear $e^+e^-$ colliders. We find out that a $0.5$ ($1$) TeV
$e^+e^-$ collider operating in the $\gamma\gamma$ mode can probe values of
$g_5^Z$ of the order of $0.15$ ($4.5 \times 10^{-2}$) for an integrated
luminosity of $10$ fb$^{-1}$. This shows that the ability to search for this
anomalous interaction of the $\gamma\gamma$ mode is better than the one of the
usual $e^+e^-$ mode, and it is similar to the ability of the $e\gamma$ mode.
