  Let $X$ be an algebraic surface of degree $5$, which is considered as a
branch cover of $\mathbb{CP}^2$ with respect to a generic projection. The
surface has a natural Galois cover with Galois group $S_5$. In this paper, we
deal with the fundamental groups of Galois covers of degree $5$ surfaces that
degenerate to nice plane arrangements; each of them is a union of five planes
such that no three planes meet in a line.
