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The detection of a super-Earth and three mini-Neptunes transiting the bright($V$ = 9.2 mag) star HD 108236 (also known as TOI-1233) was recently reportedon the basis of TESS and ground-based light curves. We perform a firstcharacterisation of the HD 108236 planetary system through high-precisionCHEOPS photometry and improve the transit ephemerides and system parameters. Wecharacterise the host star through spectroscopic analysis and derive the radiuswith the infrared flux method. We constrain the stellar mass and age bycombining the results obtained from two sets of stellar evolutionary tracks. Weanalyse the available TESS light curves and one CHEOPS transit light curve foreach known planet in the system. We find that HD 108236 is a Sun-like star with$R_{\star}=0.877\pm0.008 R_{\odot}$, $M_{\star}=0.869^{+0.050}_{-0.048}M_{\odot}$, and an age of $6.7_{-5.1}^{+4.0}$ Gyr. We report the serendipitousdetection of an additional planet, HD 108236 f, in one of the CHEOPS lightcurves. For this planet, the combined analysis of the TESS and CHEOPS lightcurves leads to a tentative orbital period of about 29.5 days. From the lightcurve analysis, we obtain radii of $1.615\pm0.051$, $2.071\pm0.052$,$2.539_{-0.065}^{+0.062}$, $3.083\pm0.052$, and $2.017_{-0.057}^{+0.052}$$R_{\oplus}$ for planets HD 108236 b to HD 108236 f, respectively. These valuesare in agreement with previous TESS-based estimates, but with an improvedprecision of about a factor of two. We perform a stability analysis of thesystem, concluding that the planetary orbits most likely have eccentricitiessmaller than 0.1. We also employ a planetary atmospheric evolution framework toconstrain the masses of the five planets, concluding that HD 108236 b and HD108236 c should have an Earth-like density, while the outer planets should hosta low mean molecular weight envelope.

CHEOPS observations of the HD 108236 planetary system: A fifth planet, improved ephemerides, and planetary radii