Stability analysis of the TOI-5624 planetary system focussing on planet f. We varied the orbital period, P_f and the eccentricity e_f (left) and the longitude of the node, Ω_f, and the inclination, I_f (right), while keeping all the remaining orbital parameters fixed at their best-fit values (Tab. 2). The step size is 0.015 day in the orbital period, 0.0025 in the eccentricity, and 1° in the longitude of the node and inclination. Plots are colour-coded according to the stability indicator calculated from the frequency analysis of the mean longitude of TOI-5624 f. Red points correspond to highly unstable orbits, while blue points correspond to orbits that are likely to be stable on Gyr timescales. The vertical dashed line (left) corresponds to the 2:1 MMR between planets e and f. The black dot along with its error bars highlights the RV-based best-fit solution P_f,RV = ${45.37}_{-0.90}^{+0.74}$ d from Tab. 2, while the black empty square indicates the more precise orbital period of planet f as inferred from the TTV+RV dynamical analysis (P_f,dyn = ${44.092}_{-0.057}^{+0.015}$ d, Table C.5). Both solutions (consistent at the 1.4σ level) are compatible with a stable configuration of the system.