  High-Curie-temperature ferromagnets are promising candidates for designing
new spintronic devices. Here we have successfully synthesized a single-crystal
sample of the itinerant ferromagnet Mn$ _{5}$Ge$_{3}$ used flux method and its
critical properties were investigated by means of bulk dc-magnetization at the
boundary between the ferromagnetic (FM) and paramagnetic (PM) phase. Critical
exponents $ \beta=0.336 \pm 0.001 $ with a critical temperature $ T_{c}=300.29
\pm 0.01 $ K and $ \gamma=1.193 \pm 0.003 $ with $ T_{c} = 300.15 \pm 0.05 $ K
are obtained by the modified Arrott plot, whereas $ \delta = 4.61 \pm 0.03 $ is
deduced by a critical isotherm analysis at $ T_{c} = 300 $ K. The
self-consistency and reliability of these critical exponents are verified by
the Widom scaling law and the scaling equations. Further analysis reveals that
the spin coupling in Mn$ _{5}$Ge$_{3}$ exhibits three-dimensional Ising-like
behavior. The magnetic exchange is found to decay as $ J(r)\approx r^{-4.855} $
and the spin interactions are extended beyond the nearest neighbors, which may
be related to different set of Mn--Mn interactions with unequal magnitude of
exchange strengths. Additionally, the existence of noncollinear spin
configurations in Mn$ _{5} $Ge$ _{3} $ results in a small deviation of obtained
critical exponents from those for standard 3D-Ising model.
