  A fifth-order nonlinear Schrodinger equation which describes one-dimensional
anisotropic Heisenberg ferromagnetic spin chain is under exploration in this
paper. Starting from the spectral analysis of the Lax pair, a Riemann-Hilbert
problem is set up. After solving the obtained Riemann-Hilbert problem with
reflectionless case, we systematically derive multisoliton solutions for the
fifth-order nonlinear Schrodinger equation. In addition, the localized
structures and dynamic behaviors of one- and two-soliton solutions are shown
vividly via a few plots.
