  The antiferromagnet Mn$_5$Si$_3$ has recently attracted attention because a
noncollinear spin arrangement has been shown to produce a topological anomalous
Hall effect and an inverse magnetocaloric effect. Here we synthesize single
crystals of Mn$_5$Si$_3$ using flux growth. We determine the phase diagram
through magnetization and measure the magnetoresistance and the Hall effect. We
find the collinear and noncollinear antiferromagnetic phases at low
temperatures and, in addition, a third magnetic phase, in between the two
antiferromagnetic phases which has ferromagnetic character. The latter magnetic
phase might be caused by strain produced by Cu inclusions that lead to quenched
fluctuations of the mixed character magnetic ordering in this compound.
