  In this paper we provide a new method to study global dynamics of planar
quasi--homogeneous differential systems. We first prove that all planar
quasi--homogeneous polynomial differential systems can be translated into
homogeneous differential systems and show that all quintic quasi--homogeneous
but non--homogeneous systems can be reduced to four homogeneous ones. Then we
present some properties of homogeneous systems, which can be used to discuss
the dynamics of quasi--homogeneous systems. Finally we characterize the global
topological phase portraits of quintic quasi--homogeneous but non--homogeneous
differential systems.
