Earth-sized planets transiting M dwarf stars present one of the best opportunities with current facilities for studying the atmospheric and bulk compositions of terrestrial worlds. Here, we statistically validate five new transiting Earth and super-Earth sized planets orbiting M dwarf stars using a combination of light curves from the Transiting Exoplanet Survey Satellite, multicolor observations from Palomar and Las Cumbres Observatory, high-resolution imaging, and stellar spectroscopy. The sample includes TOI-5716 b, an Earth-sized planet (Rp = 0.96 ± 0.05 R⊕) with a 6.766 day orbit around a metal-poor thin-disk star ([Fe/H] = −0.54 ± 0.10); TOI-5728 b, a super-Earth (Rp = 1.31 ± 0.05 R⊕) on an 11.497 day orbit; and TOI-5736 b, a larger planet (Rp = 1.56 ± 0.07 R⊕) with an ultrashort period of just 0.649 days. We also statistically validate a multiplanet system, TOI-5489, hosting two similarly sized super-Earths: TOI-5489 b (Rp = 1.40 ± 0.05 R⊕) and TOI-5489 c (Rp = 1.28 ± 0.07 R⊕) with orbital periods of 3.152 and 4.921 days, respectively. Due to their longer orbital periods, TOI-5716 b and TOI-5728 b both have equilibrium temperatures ≤ 400 K, making them useful test cases for studies of atmospheric mass loss. If TOI-5728 b is confirmed to have an Earth-like bulk composition, it would join the very small sample of rocky planets orbiting mid-to-late M dwarfs that lie below the cosmic shoreline and therefore may have retained high mean molecular weight atmospheres.