Aims: 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 higher than 5. Methods: We searched for QSOs candidates at high redshift 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 near-infrared filters). Results: 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 identification of an optically faint QSO at very high redshift (z = 5.41). The QSO has an absolute magnitude of ~-24 at the 1450 Å continuum, a bolometric luminosity of ≈2 × 1046 erg s-1, and an estimated black hole mass of ≈108 M⊙. 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. 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 object.