  Quantifying the flux of cosmic rays reaching exoplanets around M dwarfs is
essential to understand their possible effects on exoplanet habitability. Here,
we investigate the propagation of Galactic cosmic rays as they travel through
the stellar winds (astrospheres) of five nearby M dwarfs, namely: GJ 15A, GJ
273, GJ 338B, GJ 411 and GJ 887. Our selected stars each have 1 or 2 detected
exoplanets and they all have wind mass-loss rates constrained by Lyman-alpha
observations. Our simulations use a combined 1D magnetohydrodynamic (MHD)
Alfv\'en-wave-driven stellar wind model and 1D cosmic ray transport model. We
find that GJ 411 and GJ 887 have Galactic cosmic rays fluxes comparable with
Earth's at their habitable zones. On the other hand, GJ 15A, GJ 273 and GJ 338B
receive a lower Galactic cosmic ray flux in their habitable zones. All
exoplanets in our sample, with exception of GJ 15A c and GJ 411 c, have a
significantly lower flux of Galactic cosmic rays than values observed at the
Earth because they orbit closer-in. The fluxes found here can be further used
for chemical modelling of planetary atmospheres. Finally, we calculate the
radiation dose at the surface of the habitable-zone planet GJ 273 b, assuming
it has an Earth-like atmosphere. This planet receives up to 209 times less 15
MeV energy cosmic ray fluxes than values observed at Earth. However, for
high-energy cosmic rays (~ GeV), the difference in flux is only 2.3 times
smaller, which contributes to GJ 273 b receiving a significant surface
radiation dose of 0.13 mSv/yr (40% of the annual dose on Earth's surface).
