We report the discovery of HD 110113 b (TOI-755.01), a transiting mini-Neptune exoplanet on a 2.5-day orbit around the solar-analogue HD 110113 (Teff = 5730K). Using TESS photometry and HARPS radial velocities gathered by the NCORES program, we find HD 110113 b has a radius of $2.05pm0.12$ $R_oplus$ and a mass of $4.55pm0.62$ $M_oplus$. The resulting density of $2.90^{+0.75}_{-0.59}$ g cm^{-3} is significantly lower than would be expected from a pure-rock world; therefore, HD 110113 b must be a mini-Neptune with a significant volatile atmosphere. The high incident flux places it within the so-called radius valley; however, HD 110113 b was able to hold onto a substantial (0.1-1%) H-He atmosphere over its $sim4$ Gyr lifetime. Through a novel simultaneous gaussian process fit to multiple activity indicators, we were also able to fit for the strong stellar rotation signal with period $20.8pm1.2$ d from the RVs and confirm an additional non-transiting planet with a mass of $10.5pm1.2$ $M_oplus$ and a period of $6.744^{+0.008}_{-0.009}$ d.
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