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 JHK s 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 × 10 46 erg s −1 , and an estimated black hole mass of ≈10 8 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.