  We consider generalized Melvin-like solutions corresponding to Lie algebras
of rank $5$ ($A_5$, $B_5$, $C_5$, $D_5$). The solutions take place in
$D$-dimensional gravitational model with five Abelian 2-forms and five scalar
fields. They are governed by five moduli functions $H_s(z)$ ($s = 1,...,5$) of
squared radial coordinate $z=\rho^2$ which obey five differential master
equations. The moduli functions are polynomials of powers $(n_1, n_2, n_3, n_4,
n_5) = (5,8,9,8,5), (10,18,24,28,15), (9,16,21,24,25), (8,14,18,10,10)$ for Lie
algebras $A_5$, $B_5$, $C_5$, $D_5$ respectively. The asymptotic behaviour for
the polynomials at large distances is governed by some integer-valued $5 \times
5$ matrix $\nu$ connected in a certain way with the inverse Cartan matrix of
the Lie algebra and (in $A_5$ and $D_5$ cases) with the matrix representing a
generator of the $\mathbb{Z}_2$-group of symmetry of the Dynkin diagram. The
symmetry and duality identities for polynomials are obtained, as well as
asymptotic relations for solutions at large distances.
