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GDS J033218.92-275302.7 (here GS-14) is a $z\sim5.5$ galaxy detected in [CII] as part of the ALPINE survey with unusual UV spectral features that have been interpreted as signatures of either a double stellar population or of an active galactic nucleus (AGN). We exploited the multi-wavelength coverage of GS-14 to investigate the properties and the origin of its emission. We performed UV-to-NIR SED-fitting, with single/double stellar population and/or AGN component. We analyzed the VIMOS spectrum, which shows highly-ionized emission lines (Ovi, Nv, and Niv). The line properties have been compared with those observed in galaxies and AGN, and with the predictions from radiation transfer models for star-forming galaxies, AGN, and shocks. The SED-fitting provides a total stellar mass of $M_*=(4 \pm 1) \times 10^{10} M_\odot$, an age of the main stellar population of $\sim670 Myr$ and a recent short (8 Myr) burst of star formation (SF) of $\sim 90 M_\odot yr^{-1}$. The Nv line has a characteristic P-Cygni profile, which suggests a $\sim 3 Myr$ old population of stars with a mass of $\sim 5 \times10^{7} M_\odot$. The Nv profile also shows evidence for an additional component of nebular emission. The comparison of the line ratios with theoretical models allows us to associate the emission with SF or AGN, but the strong radiation field required to ionize the Ovi is more commonly related to AGN activity. We found evidence for an old and already evolved stellar population at $z\sim 5.5$ and show that the galaxy is experiencing a second short burst of SF. In addition, GS-14 carries signatures of obscured AGN activity. The AGN could be responsible for the short depletion time of this galaxy, thus making GS-14 one of the two ALPINE sources with hints of an active nucleus and an interesting target for future follow-ups.