In this article, we investigate a higher-order anisotropic Cahn-Hilliard system with a mass source (non-linear reaction term) which has applications in biology. By imposing appropriate boundary and initial conditions, we analyze the asymptotic behavior of its solutions. Initially, we demonstrate that the initial and boundary value problem generates a continuous semigroup on a suitable phase-space, which possesses a global attractor denoted by A. Subsequently, we establish the existence of an expo- nential attractor M. Consequently, the global attractor A exhibits a finite fractal dimension. MSC: 35B41, 35B45, 35K55.