To meet the thermal protection requirements of trans-domain high-Mach-number vehicles operating in extreme environments, active gas injection has been recognized as an effective thermal protection technique, while exerting a non-negligible influence on boundary-layer flow stability and transition. Meanwhile, as the flight altitude increases, the coupling effect between the emerging wall gas slip and the gas mass injection further complicates the boundary-layer instability mechanisms. In this study, a linear stability analysis framework is developed by simultaneously incorporating mass injection and wall-slip effects, and the coupled influences of these two mechanisms on the stability characteristics of a Mach 5 flat-plate boundary layer are systematically investigated under different coupling intensities. The results show that mass injection thickens the boundary layer and increases the maximum growth rates of both the first and second instability modes. It also shifts the second mode toward lower frequencies, leading to an upstream advancement of the unstable region. In contrast, wall-slip effects weaken the destabilizing influence of mass injection on the second mode and delay the synchronization location of the fast and slow acoustic modes. Conversely, wall slip simultaneously enhances the instability of the first mode, facilitating earlier transition onset when the first mode becomes dominant. For localized mass injection, when the injection strip is placed downstream of the synchronization point corresponding to the dominant unstable frequency, the growth rate and amplification factor of the unstable second mode can be effectively reduced, thereby mitigating the destabilizing influence of injection on the boundary layer. When wall-slip effects are present, the unstable region of the dominant frequency is shifted downstream. Consequently, to achieve the same stabilizing effect, the optimal injection location should be placed further downstream compared with the no-slip case. This study reveals the competing and interfering mechanisms between mass injection and wall-slip effects in the multimodal instability of hypersonic boundary layers, providing theoretical guidance for the design of high-temperature thermal protection systems and the optimization of mass injection control strategies.