  Eclipsing binaries are important benchmark objects to test and calibrate
stellar structure and evolution models. This is especially true for binaries
with a fully convective M-dwarf component for which direct measurements of
these stars' masses and radii are difficult using other techniques. Within the
potential of M-dwarfs to be exoplanet host stars, the accuracy of theoretical
predictions of their radius and effective temperature as a function of their
mass is an active topic of discussion. Not only the parameters of transiting
exoplanets but also the success of future atmospheric characterisation rely on
accurate theoretical predictions. We present the analysis of five eclipsing
binaries with low-mass stellar companions out of a sub-sample of 23, for which
we obtained ultra high-precision light curves using the CHEOPS satellite. The
observation of their primary and secondary eclipses are combined with
spectroscopic measurements to precisely model the primary parameters and derive
the M-dwarfs mass, radius, surface gravity, and effective temperature estimates
using the PYCHEOPS data analysis software. Combining these results to the same
set of parameters derived from TESS light curves, we find very good agreement
(better than 1\% for radius and better than 0.2% for surface gravity). We also
analyse the importance of precise orbits from radial velocity measurements and
find them to be crucial to derive M-dwarf radii in a regime below 5% accuracy.
These results add five valuable data points to the mass-radius diagram of
fully-convective M-dwarfs.
