  Under investigation in this work is the inverse scattering transform of the
general fifth-order nonlinear Schr\"{o}dinger equation with nonzero boundary
conditions (NZBCs), which can be reduced to several integrable equations.
Firstly, a matrix Riemann-Hilbert problem for the equation with NZBCs at
infinity is systematically investigated.Then the inverse problems are solved
through the investigation of the matrix Riemann-Hilbert problem. Thus, the
general solutions for the potentials, and explicit expressions for the
reflection-less potentials are well constructed. Furthermore, the trace
formulae and theta conditions are also presented. In particular, we analyze the
simple-pole and double-pole solutions for the equation with NZBCs. Finally, the
dynamics of the obtained solutions are graphically discussed. These results
provided in this work can be useful to enrich and explain the related nonlinear
wave phenomena in nonlinear fields.
