Context. The ESPRESSO spectrograph is a new powerful tool developed to detect and characterize extrasolar planets. Its design allows an unprecedented radial velocity precision (down to a few tens of cm s⁻¹) and long-term thermomechanical stability. Aims. We present the first stand-alone detection of an extrasolar planet by blind radial velocity search using ESPRESSO; our aim is to show the power of the instrument in characterizing planetary signals at different periodicities in long observing time spans. Methods. We used 41 ESPRESSO measurements of HD 22496 obtained within a time span of 895 days with a median photon noise of 18 cm s⁻¹. A radial velocity analysis was performed to test the presence of planets in the system and to account for the stellar activity of this K5-K7 main-sequence star. For benchmarking and comparison, we attempted the detection with 43 archive HARPS measurements and in this work we compare the results yielded by the two datasets. We also used four TESS sectors to search for transits. Results. We find radial velocity variations compatible with a close-in planet with an orbital period of P = 5.09071 ± 0.00026 days when simultaneously accounting for the effects of stellar activity on longer timescales (P_rot = 34.99_−0.53^+0.58 days). We characterize the physical and orbital properties of the planet and find a minimum mass of 5.57_−0.68^+0.73 M_⊕, right in the dichotomic regime between rocky and gaseous planets. Although not transiting according to TESS data, if aligned with the stellar spin axis, the absolute mass of the planet must be below 16 M_⊕. We find no significant evidence for additional signals in the data with semi-amplitudes above 56 cm s⁻¹ at 95% confidence. Conclusions. With a modest set of radial velocity measurements, ESPRESSO is capable of detecting and characterizing low-mass planets and constraining the presence of planets in the habitable zone of K dwarfs down to the rocky-mass regime.