We present new catalogs of M giant and M dwarf stars from the Large Sky Area Multi-Object Fibre Spectroscopic Telescope (LAMOST) data release 5 (DR5). In total, 39796 M giants and 501152 M dwarfs are identified from the classification pipeline. The template-fitting results contain M giants with 7 temperature subtypes from M0 to M6, M dwarfs with 18 temperature subtypes from K7.0 to M8.5, and 12 metallicity subclasses from dMr to usdMp. We cross-matched our M-type catalog with the Two Micron All-Sky Survey (2MASS) and Wide-field Infrared Survey Explorer (WISE) catalog to obtain infrared magnitude and colors. Adopting the distances derived from the parallaxes in Gaia DR2, the M_G_ versus (G_bp_-G_rp_)_0_ diagram shows that there are also early-type stars and white dwarf-M dwarf binaries included in our M-type stars sample, with a contamination rate of about 4.6% for M giants and 0.48% for M dwarfs. We found that CaH spectral indices are an efficient selection criteria for carbon stars. A total of 289 carbon stars were identified from the M giants sample, and further confirmed by LAMOST spectra.