[Abridged] 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 TESS orbiting the nearby, bright, late F-type star HD 5278 (TOI-130) with a period $P_{rm b}=14.3$. We use 43 ESPRESSO high-resolution spectra and broad-band photometry information to derive accurate stellar atmospheric and physical parameters of HD 5278. We exploit the TESS light curve (LC) and spectroscopic diagnostics to gauge the impact of stellar activity on the ESPRESSO RVs. We perform a joint ESPRESSO RVs + TESS LC analysis using fully Bayesian frameworks to determine the system parameters. The updated stellar parameters of HD 5278 are T$_mathrm{eff}=6203pm64$ K, $log g =4.50pm0.11$ dex, [Fe/H]=$-0.12pm0.04$ dex, M$_star=1.126_{-0.035}^{+0.036}$ M$_odot$ and R$_star=1.194_{-0.016}^{+0.017}$ R$_odot$. We determine HD 5278 bs mass and radius to be $M_{rm b} = 7.8_{-1.4}^{+1.5}$ M$_oplus$ and $R_{rm b} = 2.45pm0.05$ R$_oplus$. The derived mean density, $varrho_{rm b} = 2.9_{-0.5}^{+0.6}$ g cm$^{-3}$, is consistent with a bulk composition with a substantial ($sim30%$) water mass fraction and a gas envelope comprising $sim17%$ of the measured radius. Given the host brightness and irradiation levels, HD 5278 b is one of the best targets orbiting 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 $P_{rm c}=40.87_{-0.17}^{+0.18}$ days and a minimum mass $M_{rm c}sin i_{rm c} =18.4_{-1.9}^{+1.8}$ M$_oplus$. We study emerging trends in the growing population of transiting sub-Neptunes, and provide statistical evidence for a low occurrence of close-in, $10-15$ M$_oplus$ companions around G-F primaries with $T_mathrm{eff}gtrsim5500$ K.
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