We aim to illustrate the potentiality of the Advanced Large, Homogeneous Area, Medium-Band Redshift Astronomical (ALHAMBRA) survey to investigate the high redshift universe through the detection of quasi stellar objects (QSOs) at redshifts larger than 5. The search for z>5 QSOs candidates was done by fitting an extensive library of spectral energy distributions --including active and non-active galaxy templates as well as stars-- to the photometric database of the ALHAMBRA survey (composed of 20 optical medium-band plus the 3 broad-band JHKs filters). Our selection over ~1 square degree of ALHAMBRA data (~1/4 of the total area covered by the survey), combined with GTC/OSIRIS spectroscopy, has yielded the identification of an optically faint QSO at very high redshift (z = 5.41). The QSO has an absolute magnitude of ~-24 at the 1450{AA} continuum, a bolometric luminosity of ~2x10^46 erg/s and an estimated black hole mass of ~10^8 Msolar. This QSO adds itself to a reduced number of known UV faint sources at these redshifts. The preliminary derived space density is compatible with the most recent determinations of the high-z QSO luminosity functions (QLF). This new detection shows how ALHAMBRA, as well as forthcoming well designed photometric surveys, can provide a wealth of information on the origin and early evolution of this kind of objects.