  We study the five-body decays $\mu^- \to e^- e^+ e^- \nu_{\mu} \bar{\nu}_{e}$
and $\tau^- \to \ell^- \ell'^+\ell'^-\nu_{\tau}\bar{\nu}_{\ell}$ for $\ell,
\ell'=e, \mu$ within the Standard Model (SM) and in a general effective field
theory description of the weak interactions at low energies. We compute the
branching ratios and compare our results with two previous, mutually
discrepant, SM calculations. By assuming a general structure for the weak
currents we derive the expressions for the energy and angular distributions of
the three charged leptons when the decaying lepton is polarized, which will be
useful in precise tests of the weak charged current at Belle II. In these
decays, leptonic $\mathbf{T}$-odd correlations in triple products of spin and
momenta --which may signal time reversal violation in the leptonic sector-- are
suppressed by the tiny neutrino masses. Therefore, a measurement of such
$\mathbf{T}$-violating observables would be associated to neutrinoless lepton
flavor violating (LFV) decays, where this effect is not extremely suppressed.
We also study the backgrounds that the SM five-lepton lepton decays constitute
to searches of LFV $L^- \to \ell^- \ell'^+\ell'^-$ decays. Searches at high
values of the invariant mass of the $\ell'^+\ell'^-$ pair look the most
convenient way to overcome the background.
