  Investigating the off-diagonal components of the conductivity and
thermoelectric tensor of materials hosting complex antiferromagnetic structures
has become a viable method to reveal the effects of topology and chirality on
the electronic transport in these systems. In this respect, Mn$_5$Si$_3$ is an
interesting metallic compound that exhibits several antiferromagnetic phases
below 100 K with different collinear and noncollinear arrangements of Mn
magnetic moments. Previous investigations have shown that the transitions
between the various phases give rise to large changes of the anomalous Hall
effect. Here, we report measurements of the anomalous Nernst effect of
Mn$_5$Si$_3$ single crystals. Below 25 K we observe a sign change of the
zero-field Nernst signal with a concomitant decrease of the Hall signal and a
gradual reduction of the remanent magnetization which we attribute to a subtle
rearrangement of the magnetic moment configuration at low temperatures.
