Abstract: We present measurements of the branching fractions of three-prong and five-prong tau decay modes using a sample of 430 million tau lepton pairs, corresponding to an integrated luminosity of 468 fb(-1), collected with the BABAR detector at the PEP-II asymmetric-energy e_e storage rings at SLAC National Accelerator Laboratory. The tau(-) -> (3 pi)(-) eta nu(tau), tau(-) -> (3 pi)(-) omega nu(tau), and tau(-) f(1) (1285)nu(tau) branching fractions are presented, as well as a new limit on the branching fraction of the second-class current decay tau(-) -> pi(-) eta'(958)nu(tau). We search for the decay mode tau(-) -> K- eta'(958)nu(tau) and for five-prong decay modes with kaons, and place the first upper limits on their branching fractions.