Context. A large sample of long-period giant planets has been discovered thanks to long-term radial velocity surveys, but only a few dozen of these planets have a precise radius measurement. Transiting gas giants are crucial targets for the study of atmospheric composition across a wide range of equilibrium temperatures and, more importantly, for shedding light on the formation and evolution of planetary systems. Indeed, compared to hot Jupiters, the atmospheric properties and orbital parameters of cooler gas giants are unaltered by intense stellar irradiation and tidal effects. Aims. We aim to identify long-period planets in the Transiting Exoplanet Survey Satellite (TESS) data as single or duo-transit events. Our goal is to solve the orbital periods of TESS duo-transit candidates with the use of additional space-based photometric observations and to collect follow-up spectroscopic observations in order to confirm the planetary nature and measure the mass of the candidates. Methods. We use the CHaracterising ExOPlanet Satellite (CHEOPS) to observe the highest-probability period aliases in order to discard or confirm a transit event at a given period. Once a period is confirmed, we jointly model the TESS and CHEOPS light curves along with the radial velocity datasets to measure the orbital parameters of the system and obtain precise mass and radius measurements. Results. We report the discovery of a long-period transiting Neptune-mass planet orbiting the G7-type star TOI-5678. Our spectroscopic analysis shows that TOI-5678 is a star with a solar metallicity. The TESS light curve of TOI-5678 presents two transit events separated by almost two years. In addition, CHEOPS observed the target as part of its Guaranteed Time Observation program. After four non-detections corresponding to possible periods, CHEOPS detected a transit event matching a unique period alias. Follow-up radial velocity observations were carried out with the ground-based high-resolution spectrographs CORALIE and HARPS. Joint modeling reveals that TOI-5678 hosts a 47.73 day period planet, and we measure an orbital eccentricity consistent with zero at 2σ. The planet TOI-5678 b has a mass of 20 ± 4 Earth masses (M_⊕) and a radius of 4.91 ± 0.08 R_⊕ Using interior structure modeling, we find that TOI-5678 b is composed of a low-mass core surrounded by a large H/He layer with a mass of 3.2^±1.7_−1.3 M_⊕. Conclusions. TOI-5678 b is part of a growing sample of well-characterized transiting gas giants receiving moderate amounts of stellar insolation (11 S_⊕). Precise density measurement gives us insight into their interior composition, and the objects orbiting bright stars are suitable targets to study the atmospheric composition of cooler gas giants.