  The weight of a subgraph $H$ in $G$ is the sum of the degrees in $G$ of
vertices of $H$. The {\em height} of a subgraph $H$ in $G$ is the maximum
degree of vertices of $H$ in $G$. A star in a given graph is minor if its
center has degree at most five in the given graph. Lebesgue (1940) gave an
approximate description of minor $5$-stars in the class of normal plane maps
with minimum degree five. In this paper, we give two descriptions of minor
$5$-stars in plane graphs with minimum degree five. By these descriptions, we
can extend several results and give some new results on the weight and height
for some special plane graphs with minimum degree five.
