  A \emph{book-embedding} of a graph $G$ is an embedding of vertices of $G$
along the spine of a book, and edges of $G$ on the pages so that no two edges
on the same page intersect. the minimum number of pages in which a graph can be
embedded is called the \emph{page number}. The book-embedding of graphs may be
important in several technical applications, e.g., sorting with parallel
stacks, fault-tolerant processor arrays design, and layout problems with
application to very large scale integration (VLSI). Bernhart and Kainen firstly
considered the book-embedding of the planar graph and conjectured that its page
number can be made arbitrarily large [JCT, 1979, 320-331]. Heath [FOCS84] found
that planar graphs admit a seven-page book embedding. Later, Yannakakis proved
that four pages are necessary and sufficient for planar graphs in [STOC86].
Recently, Bekos et al. [STACS14] described an $O(n^{2})$ time algorithm of
two-page book embedding for 4-planar graphs. In this paper, we embed 5-planar
graphs into a book of three pages by an $O(n^{2})$ time algorithm.
