  Fe$_{5-x}$GeTe$_2$ is a centrosymmetric, layered van der Waals (vdW)
ferromagnet that displays Curie temperatures $T_c$ (270-330 K) that are within
the useful range for spintronic applications. However, little is known about
the interplay between its topological spin textures (e.g., merons, skyrmions)
with technologically relevant transport properties such as the topological Hall
effect (THE), or topological thermal transport. Here, we show via
high-resolution Lorentz transmission electron microscopy that merons and
anti-meron pairs coexist with N\'{e}el skyrmions in Fe$_{5-x}$GeTe$_2$ over a
wide range of temperatures and probe their effects on thermal and electrical
transport. We detect a THE, even at room $T$, that senses merons at higher $T$s
as well as their coexistence with skyrmions as $T$ is lowered indicating an
on-demand thermally driven formation of either type of spin texture.
Remarkably, we also observe an unconventional THE in absence of Lorentz force
and attribute it to the interaction between charge carriers and magnetic
field-induced chiral spin textures. Our results expose Fe$_{5-x}$GeTe$_2$ as a
promising candidate for the development of applications in skyrmionics/meronics
due to the interplay between distinct but coexisting topological magnetic
textures and unconventional transport of charge/heat carriers.
