A search for the decay of the τ lepton to five charged and two neutral pions is performed using data collected by the BABAR detector at the PEP-II asymmetric-energy e+e- collider. The analysis uses 232fb-1 of data at center-of-mass energies on or near the Υ(4S) resonance. We observe 10 events with an expected background of 6.5-1.4+2.0 events. In the absence of a signal, we set the limit on the branching ratio B(τ-→3π- 2π+2π0ντ)<3.4×10-6 at the 90% confidence level. This is a significant improvement over the previously established limit. In addition, we search for the decay mode τ-→2ωπ-ντ. We observe 1 event with an expected background of 0.4+1.0-0.4 events and calculate the upper limit B(τ-→2ωπ-ντ)<5.4×10-7 at the 90% confidence level. This is the first upper limit for this mode. © 2006 The American Physical Society.