  This paper is concerned with the construction of the fifth-order generalized
Heisenberg supermagnetic models. We also investigate the integrable structure
and properties of the supersymmetric systems. We establish their gauge
equivalent equations with the gauge transformation for two quadratic
constraints, i.e., the super fifth-order nonlinear Schr\"{o}dinger equation and
the fermionic fifth-order nonlinear Schr\"{o}dinger equation, respectively.
