  We present the discovery from the TESS mission of two giant planets
transiting M dwarf stars: TOI 4201 b and TOI 5344 b. We also provide precise
radial velocity measurements and updated system parameters for three other M
dwarfs with transiting giant planets: TOI 519, TOI 3629 and TOI 3714. We
measure planetary masses of 0.525 +- 0.064 M_J, 0.243 +- 0.020 M_J, 0.689 +-
0.030 M_J, 2.57 +- 0.15 M_J, and 0.412 +- 0.040 M_J for TOI 519 b, TOI 3629 b,
TOI 3714 b, TOI 4201 b, and TOI 5344 b, respectively. The corresponding stellar
masses are 0.372 +- 0.018 M_s, 0.635 +- 0.032 M_s, 0.522 +- 0.028 M_s, 0.625 +-
0.033 M_s and 0.612 +- 0.034 M_s. All five hosts have super-solar
metallicities, providing further support for recent findings that, like for
solar-type stars, close-in giant planets are preferentially found around
metal-rich M dwarf host stars. Finally, we describe a procedure for accounting
for systematic errors in stellar evolution models when those models are
included directly in fitting a transiting planet system.
