  Encouraged by the observation of the pentaquark states $P^+_c(4380)$ and
$P^+_c(4450)$, we propose a novel color flux-tube structure, pentagonal state,
for pentaquark states within the framework of color flux-tube mode involving a
five-body confinement potential. Numerical results on the heavy pentaquark
states indicate that the states with three color flux-tube structures, diquark,
octet and pentagonal structures, have the close masses, which can therefore be
called QCD isomers analogous to isomers in Chemistry. The pentagonal structure
has lowest energy. The state $P^+_c(4380)$ can be described as the compact
pentaquark state $uudc\bar{c}$ with the pentagonal structure and
$J^P=\frac{3}{2}^-$ in the color flux-tube model. The state $P^+_c(4450)$ can
not be accommodated into the color flux-tube model. The heavy pentaquark states
$uudc\bar{b}$, $uudb\bar{c}$ and $uudb\bar{b}$ are predicted in the color
flux-tube model. The five-body confinement potential basing on the color
flux-tube picture as a collective degree of freedom is a dynamical mechanism in
the formation of the compact heavy pentaquark states.
