  Separation energies of light $\Lambda$ hypernuclei ($A\leq 5$) and their
theoretical uncertainties are investigated. Few-body calculations are performed
within the Faddeev-Yakubovsky scheme and the no-core shell model. Thereby,
modern and up-to-date $N\!N$ and $Y\!N$ potentials derived within chiral
effective field theory are employed. % It is found that the numerical
uncertainties of the few-body methods are well under control and an accuracy of
around $1$ keV for the hypertriton and of less than $20$ keV for the separation
energies of the $^4_{\Lambda}\mathrm{He}$ and $^5_{\Lambda}\mathrm{He}$
hypernuclei can be achieved. Variations caused by differences in the $N\!N$
interaction are in the order of $10$ keV for $^3_{\Lambda}\mathrm{H}$ and no
more than $110$ keV for $A=4,\,5$ $\Lambda$ hypernuclei, when recent
high-precision potentials up to fifth order in the chiral expansion are
employed. The variations are smaller than expected contributions from chiral
$Y\!N\!N$ three-body forces (3BFs) which arise at the chiral order of
state-of-the-art $Y\!N$ potentials. Estimates for those 3BFs are deduced from a
study of the truncation uncertainties in the chiral expansion.
