The total decay width of a particle, $\Gamma$, is proportional to the fifth power of its mass, $m$, $$ \Gamma \propto m^5$$
We also know that the dominant decays of the tau lepton are $$\tau^- \to \nu_\tau e^- \nu_e$$ $$\tau^- \to \nu_\tau \mu^- \nu_\mu$$ $$\tau^- \to \nu_\tau \ du$$ with branching ratios of approximately 20%, 20% and 60%, respectively.
Given that the lifetime of a muon is known to be $\tau_\mu$ I have been told that the lifetime of the tau is
$$\tau_{\tau}=\frac{1}{5}\left(\frac{m_{\mu}}{m_{\tau}}\right)^{5} \tau_{\mu}=1.48 \times 10^{-7} \tau_{\mu}$$
I am unsure where the 1/5 factor has come from, any explanation would be appreciated.