Context. Transiting sub-Neptune-type planets, with radii approximately between 2 and 4 R_⊕, are of particular interest as their study allows us to gain insight into the formation and evolution of a class of planets that are not found in our Solar System. Aims. We exploit the extreme radial velocity (RV) precision of the ultra-stable echelle spectrograph ESPRESSO on the VLT to unveil the physical properties of the transiting sub-Neptune TOI-130 b, uncovered by the TESS mission orbiting the nearby, bright, late F-type star HD 5278 (TOI-130) with a period of P_b = 14.3 days. Methods. We used 43 ESPRESSO high-resolution spectra and broad-band photometry information to derive accurate stellar atmospheric and physical parameters of HD 5278. We exploited the TESS light curve and spectroscopic diagnostics to gauge the impact of stellar activity on the ESPRESSO RVs. We performed separate as well as joint analyses of the TESS photometry and the ESPRESSO RVs using fully Bayesian frameworks to determine the system parameters. Results. Based on the ESPRESSO spectra, the updated stellar parameters of HD 5278 are T_eff = 6203 ± 64 K, log g = 4.50 ± 0.11 dex, [Fe/H] = −0.12 ± 0.04 dex, M_⋆ = 1.126_−0.035^+0.036 M_⊙, and R_⋆ = 1.194_−0.016^+0.017 R_⊙. We determine HD 5278 b’s mass and radius to be M_b = 7.8_−1.4^+1.5 M_⊕ and R_b = 2.45 ± 0.05R_⊕. The derived mean density, ϱ_b = 2.9_−0.5^+0.6 g cm⁻³, is consistent with the bulk composition of a sub-Neptune with a substantial (~ 30%) water mass fraction and with a gas envelope comprising ~17% of the measured radius. Given the host brightness and irradiation levels, HD 5278 b is one of the best targetsorbiting G-F primaries for follow-up atmospheric characterization measurements with HST and JWST. We discover a second, non-transiting companion in the system, with a period of P_c = 40.87_−0.17^+0.18 days and a minimum mass of M_c sin i_c = 18.4_−1.9^+1.8 M_⊕. We study emerging trends in parameters space (e.g., mass, radius, stellar insolation, and mean density) of the growing population of transiting sub-Neptunes, and provide statistical evidence for a low occurrence of close-in, 10 − 15M_⊕ companions around G-F primaries with T_eff ≳ 5500 K.