Context. Low mass stars are currently the best targets for searches for rocky planets in the habitable zone of their host star. Over the last 13 years, precise radial velocities measured with the HARPS spectrograph have identified over a dozen super-Earths and Earth-mass planets (msin i<10Mearth ) around M dwarfs, with a well understood selection function. This well defined sample informs on their frequency of occurrence and on the distribution of their orbital parameters, and therefore already constrains our understanding of planetary formation. The subset of these low-mass planets that were found within the habitable zone of their host star also provide prized targets for future atmospheric biomarkers searches. Aims. We are working to extend this planetary sample to lower masses and longer periods through dense and long-term monitoring of the radial velocity of a small M dwarf sample. Methods. We obtained large numbers of HARPS spectra for the M dwarfs GJ 3138, GJ 3323, GJ 273, GJ 628 and GJ 3293, from which we derived radial velocities (RVs) and spectroscopic activity indicators. We searched them for variabilities, periodicities, Keplerian modulations and correlations, and attribute the radial-velocity variations to combinations of planetary companions and stellar activity. Results. We detect 12 planets, of which 9 are new with masses ranging from 1.17 to 10.5 Mearth . Those planets have relatively short orbital periods (P<40 d), except two of them with periods of 217.6 and 257.8 days. Among these systems, GJ 273 harbor two planets with masses close to the one of the Earth. With a distance of 3.8 parsec only, GJ 273 is the second nearest known planetary system - after Proxima Centauri - with a planet orbiting the circumstellar habitable zone.
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