Recent technological advances in cavity quantum electrodynamics (CQED) are paving the way to utilise multiple quantum emitters confined in a single optical cavity. In such systems it is crucially important to control the quantum mechanical coupling of individual emitters to the cavity mode. In this regard, combining ion trap technologies with CQED provides a particularly promising approach due to the well-established motional control over trapped ions. Here we experimentally demonstrate coupling of up to five trapped ions in a string to a high-finesse optical cavity. By changing the axial position and spacing of the ions in a fully deterministic manner, we systematically characterise their coupling to the cavity mode through visibility measurements of the cavity emission. In good agreement with the theoretical model, the results demonstrate that the geometrical configuration of multiple trapped ions can be manipulated to obtain optimal cavity coupling. Our system presents a new ground to explore CQED with multiple quantum emitters, enabled by the highly controllable collective light-matter interaction.