  The crystal-field (CF) splitting of the $^6H_{5/2}$ Hund's rule ground state
of Sm$^{3+}$ in the strongly correlated topological insulator SmB$_6$ has been
determined with high resolution resonant inelastic x-ray scattering (RIXS) at
the Sm M$_5$ edge. The valence selectivity of RIXS allows isolating the
crystal-field-split excited multiplets of the Sm$^{3+}$ (4$f^5$) configuration
from those of Sm$^{2+}$ (4$f^6$) in intermediate valent SmB$_6$. The very large
energy range of RIXS allows the crystal-field analysis of a high lying
multiplet at about 2.4\,eV that has the same total angular momentum $J$ as the
ground state so that ambiguities due to the elastic tail can be avoided. We
find that the $\Gamma_7$ doublet and $\Gamma_8$ quartet of the $^6H_{5/2}$
Hund's rule ground state are split by
$\Delta^{CF}_{^6H_{5/2}}$\,=\,20$\pm$10\,meV which sets an upper limit for the
4$f$ band width. This indicates an extremely large mass renormalization from
the band structure value, pointing out the need to consider the coefficients of
fractional parentage for the hopping of the 4$f$ electrons.
