Comparing the properties of planets orbiting the same host star, and thus formed from the same accretion disc, helps in constraining theories of exoplanet formation and evolution. As a result, the scientific interest in multi-planetary systems is growing with the increasing number of detections of planetary companions. We report the characterisation of a multi-planetary system composed of five exoplanets orbiting the K-dwarf HD 23472 (TOI-174). In addition to the two super-Earths that were previously confirmed, we confirm and characterise three Earth-size planets in the system using ESPRESSO radial velocity observations. The planets of this compact system have periods of Pd~3.98, Pe~7.90, Pf~12.16, Pb~17.67 and Pc~29.80-days and radii of Rd~0.75, Re~0.82, Rf~1.13, Rb~2.01, and, Rc~1.85R_{Earth}. Because of its small size, its proximity to planet d transit, and close resonance with planet d, planet e was only recently found. The planetary masses were estimated to be M_d=0.54+/-0.22, M_e_=0.76+/-0.30, M_f_=0.64+/-0.46, M_b_=8.42+/-0.84, and M_c_=3.37+/-0.92M_{Earth}. These planets are among the lightest planets, with masses measured using the radial velocity method, demonstrating the very high precision of the ESPRESSO spectrograph. We estimated the composition of the system five planets and found that their gas and water mass fractions increase with stellar distance, suggesting that the system was shaped by irradiation. The high density of the two inner planets rho_d=7.5+/-3.9 and rho_e_=7.5+/-3.9g/cm^3^ indicates that they are likely to be super-Mercuries. This is supported by the modelling of the internal structures of the planets, which also suggests that the three outermost planets have significant water or gas content. If the existence of two super-Mercuries in the system is confirmed, this system will be the only one known to feature two super-Mercuries, making it an excellent testing bed for theories of super-Mercuries formation. Furthermore, the system is close to a Laplace resonance, and further monitoring could shed light on how it was formed. Its uniqueness and location in the continuous viewing zone of the James Webb space telescope will make it a cornerstone of future in-depth characterisations.