  We report a detailed study of the magnetic, transport, and thermodynamic
properties of Ce$_2$Te$_5$ single crystals, a layered $f$-electron van der
Waals magnet. Four consecutive transitions at $\sim$ 5.2, 2.1, 0.9, and 0.4 K
were observed in the $ac$-plane electrical resistivity $\rho$(T), which were
further confirmed in specific heat $C_\textrm{p}$(T) measurements. Analysis of
the magnetic susceptibility $\chi$(T), the magnetic-field variation of
$\rho$(T), and the increase of the first transition temperature ($T_\textrm{c}
\sim$ 5.2 K) with applied magnetic field indicates ferromagnetic order, while
the decrease of the other transitions with field suggests different states with
dominant antiferromagnetic interactions below $T_2 \sim$ 2.1 K, $T_3 \sim$ 0.9
K, and $T_4$ = 0.4 K. Critical behavior analysis around $T_\textrm{c}$ that
gives critical exponents $\beta = 0.31(2)$, $\gamma = 0.99(2)$, $\delta =
4.46(1)$, $T_\textrm{c} = 5.32(1)$ K indicates that Ce$_2$Te$_5$ shows a
three-dimensional magnetic critical behavior. Moreover, the Hall resistivity
$\rho_{\textrm{xy}}$ indicates that Ce$_2$Te$_5$ is a multi-band system with a
relatively high electron mobility $\sim 2900$ cm$^2$ V$^{-1}$ s$^{-1}$ near
$T_\textrm{c}$, providing further opportunities for future device applications.
