An upper limit for the ττ–neutrino mass has been determined from the decay τ→5π±νττ→5π±ντ using data collected with the OPAL detector from 1991 to 1995 in e+e−e+e− collisions at s√≈MZs≈MZ. A limit of 43.2 MeV at 95% CL is obtained using a two–dimensional method in the 5π5π invariant mass and energy distribution from 22 selected events. Combining this result with OPAL's previously published measurement using τ+τ−→3h±ν¯τ+3h∓νττ+τ−→3h±ν¯τ+3h∓ντ decays, a new combined limit of mντ<27.6mντ<27.6 MeV (95% CL) is obtained.