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The HD108236 system was first announced with the detection of four small planets based on TESS data. Shortly after, the transit of an additional planet with a period of 29.54d was serendipitously detected by CHEOPS. In this way, HD108236 (V=9.2) became one of the brightest stars known to host five small transiting planets (R$_p$<3R$_{\oplus}$). We characterize the planetary system by using all the data available from CHEOPS and TESS space missions. We use the flexible pointing capabilities of CHEOPS to follow up the transits of all the planets in the system, including the fifth transiting body. After updating the host star parameters by using the results from Gaia eDR3, we analyzed 16 and 43 transits observed by CHEOPS and TESS, respectively, to derive the planets physical and orbital parameters. We carried out a timing analysis of the transits of each of the planets of HD108236 to search for the presence of transit timing variations. We derived improved values for the radius and mass of the host star (R$_{\star}$=0.876$\pm$0.007 R$_{\odot}$ and M$_{\star}$=0.867$_{-0.046}^{+0.047}$ M$_{\odot}$). We confirm the presence of the fifth transiting planet f in a 29.54d orbit. Thus, the system consists of five planets of R$_b$=1.587$\pm$0.028, R$_c$=2.122$\pm$0.025, R$_d$=2.629$\pm$0.031, R$_e$=3.008$\pm$0.032, and R$_f$=1.89$\pm$0.04 [R$_{\oplus}$]. We refine the transit ephemeris for each planet and find no significant transit timing variations for planets c, d, and e. For planets b and f, instead, we measure significant deviations on their transit times (up to 22 and 28 min, respectively) with a non-negligible dispersion of 9.6 and 12.6 min in their time residuals. We confirm the presence of planet f and find no significant evidence for a potential transiting planet in a 10.9d orbital period, as previously suggested. Full abstract in the PDF file.