Aims: The aim of the project is to find the stars closest to the Sun and to contribute to the completion of the stellar and substellar census of the solar neighbourhood. Methods: We identified a new late-M dwarf within 5 pc, looking for high proper motion sources in the 2MASS-WISE cross-match. We collected astrometric and photometric data available from public large-scale surveys. We complemented this information with low-resolution (R ~ 500) optical (600-1000 nm) and near-infrared (900-2500 nm) spectroscopy with instrumentation on the European Southern Observatory New Technology Telescope to confirm the nature of our candidate. We also present a high-quality medium-resolution VLT/X-shooter spectrum covering the 400 to 2500 nm wavelength range. Results: We classify this new neighbour as an M7.0 ± 0.5 dwarf using spectral templates from the Sloan Digital Sky Survey and spectral indices. Lithium absorption at 670.8 nm is not detected in the X-shooter spectrum, indicating that the M7 dwarf is older than 600 Myr and more massive than 0.06 M⊙. We also derive a trigonometric distance of 4.4+0.5-0.4 pc, in agreement with the spectroscopic distance estimate, making 2MASS J154043.42-510135.7 (2M1540) the nearest M7 dwarf to the Sun. This trigonometric distance is somewhat closer than the ~6 pc distance reported by the ALLWISE team, who independently identified this object recently. This discovery represents an increase by 25% in the number of M7-M8 dwarfs already known at distances closer than 8 pc from our Sun. We derive a density of ρ = 1.9 ± 0.9 × 10-3 pc-3 for M7 dwarfs in the 8 pc volume, a value similar to those quoted in the literature. Conclusions: This new ultracool dwarf is among the 50 closest systems to the Sun, demonstrating that our current knowledge of the stellar census within the 5 pc sample remains incomplete. 2M1540 represents a unique opportunity to search for extrasolar planets around ultracool dwarfs due to its proximity and brightness. Based on observations collected at the European Organisation for Astronomical Research in the Southern Hemisphere, Chile.