<p>Hyperlipidemia is recognized as a significant health concern in the human body. In this study, a novel mathematical framework is developed to investigate targeted therapeutic strategies for reducing hyperlipidemia through a fifth-compartment mathematical model. The model consists of five compartments: the liver, blood, gallbladder, intestine, and tissue. To address hyperlipidemia, direct drug administration into the bloodstream is incorporated. Potential treatments for lowering cholesterol levels in the blood and tissue are explored, contributing to advancements in medical research. Sensitivity analysis is performed to determine the impact of various parameters on equilibrium stability. Stability tests evaluate the model’s long-term stability, ensuring greater accuracy in predictive modeling. The variation in cholesterol levels and drug concentration over time is analyzed using MATLAB software, with graphical results demonstrating a gradual decline in cholesterol levels following drug administration. Both analytical and numerical assessments confirm the model’s effectiveness in characterizing cholesterol transport and optimizing therapeutic strategies for hyperlipidemia management.</p>