Context. The existence of lithium-rich low-mass red giant stars still represents a challenge for stellar evolution models. Stellar clusters are privileged environments for this kind of investigation. Aims. To investigate the chemical abundance pattern of the old open cluster Trumpler 5, we observed a sample of four red-clump stars with high-resolution optical spectrographs. One of them (#3416) reveals extremely strong lithium lines in its spectrum. Methods. One-dimensional, local thermodynamic equilibrium analysis was performed on the spectra of the observed stars. A 3D-NLTE analysis was performed to derive the lithium abundance of star #3416. Results. Star #3416 is super Li-rich with A(Li) = 3.75 dex. The lack of 6Li enrichment (6Li/7Li < 2%), the low carbon isotopic ratio (12C/13C = 14 ± 3), and the lack of evidence for radial velocity variation or enhanced rotational velocity (vsini = 2.8  km s-1) all suggest that lithium production has occurred in this star through the Cameron & Fowler mechanism. Conclusions. We identified a super Li-rich core helium-burning, red-clump star in an open cluster. Internal production is the most likely cause of the observed enrichment. Given the expected short duration of a star’s Li-rich phase, enrichment is likely to have occurred at the red clump or in the immediately preceding phases, namely during the He-flash at the tip of the red giant branch (RGB) or while ascending the brightest portion of the RGB.