We present the discovery of five late-type T dwarfs identified with the Wide-field Infrared Survey Explorer (WISE). Low-resolution near-infrared spectroscopy obtained with the Magellan Folded-port InfraRed Echellette (FIRE) reveal strong water and methane absorption in all five sources, and spectral indices and comparison to spectral templates indicate classifications ranging from T5.5 to T8.5:. The spectrum of the latest-type source, WISE J1812+2721, is an excellent match to that of the T8.5 companion brown dwarf Wolf 940B. WISE-based spectrophotometric distance estimates place these T dwarfs at 12-13 pc from the Sun, assuming they are single. Preliminary fits of the spectral data to the atmosphere models of Saumon & Marley indicate effective temperatures ranging from 600 K to 930 K, both cloudy and cloud-free atmospheres, and a broad range of ages and masses. In particular, two sources show evidence of both low surface gravity and cloudy atmospheres, tentatively supporting a trend noted in other young brown dwarfs and exoplanets. In contrast, the high proper motion T dwarf WISE J2018-7423 exhibits a suppressed K-band peak and blue spectrophotometric J-K colors indicative of an old, massive brown dwarf; however, it lacks the broadened Y-band peak seen in metal-poor counterparts. These results illustrate the broad diversity of low-temperature brown dwarfs that will be uncovered with WISE.