  Trigonal Cr5Te8, a self-intercalated van der Waals ferromagnet with an out of
plane magnetic anisotropy, has long been known to crystallise in a
centrosymmetric structure. Through detailed structural analysis together with
second harmonic generation experiments, we show that the compound actually
adopts a non-centrosymmetric structure. A large anomalous Hall conductivity of
102 {\Omega}^(-1) cm^(-1) at low temperature stems from intrinsic origin, which
is larger than any previously reported values in bulk Cr-Te system. In
addition, we observe a hump-like feature in the field-dependent Hall
resistivity data, resembling a typical topological Hall signal. We demonstrate
that the feature is highly tunable and is not related to topological Hall
effect even though we observe N\'eel-type skyrmions by Lorentz transmission
electron microscopy which is consistent with the non-centrosymmetric structure
of the compound.
