Context. The first generation of stars formed in the Galaxy left behind the chemical signatures of their nucleosynthesis in the interstellar medium, visible today in the atmospheres of low-mass stars that formed afterwards. Sampling the chemistry of those low-mass provides insight into the first stars. Aims: We aim to increase the samples of stars with extremely low metal abundances, identifying ultra metal-poor stars from spectra with modest spectral resolution and signal-to-noise ratio (S/N). Achieving this goal involves deriving reliable metallicities and carbon abundances from such spectra. Methods: We carry out follow-up observations of faint, V > 19, metal-poor candidates selected from SDSS spectroscopy and observed with the Optical System for Imaging and low-Intermediate-Resolution Integrated Spectroscopy (OSIRIS) at GTC. The SDSS and follow-up OSIRIS spectra were analyzed using the FERRE code to derive effective temperatures, surface gravities, metallicities and carbon abundances. In addition, a well-known extremely metal-poor star has been included in our sample to calibrate the analysis methodology. Results: We observed and analyzed five metal-poor candidates from modest-quality SDSS spectra. All stars in our sample have been confirmed as extremely metal-poor stars, in the [Fe/H] < -3.3 regime. We report the recognition of J173403+644632, a carbon-enhanced ultra metal-poor dwarf star with [Fe/H] = -4.3 and [C/Fe] = + 3.1. Based on observations made with the Gran Telescopio Canarias (GTC), installed in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias, on the island of La Palma. Programme ID GTC2E-16A and ID GTC65-16B.