  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.
