A subgraph of a plane graph is light if the sum of the degrees of the vertices of the subgraph in the graph is small. It is known that a plane graph of minimum face size 5 contains light paths and a light pentagon. In this paper we show that every plane graph of minimum face size 5 contains also a light star $K_{1,3}$ and we present a structural result concerning the existence of a pair of adjacent faces with degree-bounded vertices