We present abundances for seven stars in the (extremely) low-metallicity tail of the Sculptor dwarf spheroidal galaxy, from spectra taken with X-shooter on the ESO VLT. Targets were selected from the Ca II triplet (CaT) survey of the dwarf abundances and radial velocities team (DART) using the latest calibration. Of the seven extremely metal-poor candidates, five stars are confirmed to be extremely metal-poor (i.e., [Fe/H] < -3 dex), with [Fe/H] = -3.47 ± 0.07 for our most metal-poor star. All have [Fe/H] ≤ -2.5 dex from the measurement of individual Fe lines. These values are in agreement with the CaT predictions to within error bars. None of the seven stars is found to be carbon-rich. We estimate a 2-13% possibility of this being a pure chance effect, which could indicate a lower fraction of carbon-rich extremely metal-poor stars in Sculptor compared to the Milky Way halo. The [α/Fe] ratios show a range from +0.5 to -0.5, a larger variation than seen in Galactic samples although typically consistent within 1-2σ. One star seems mildly iron-enhanced. Our program stars show no deviations from the Galactic abundance trends in chromium and the heavy elements barium and strontium. Sodium abundances are, however, below the Galactic values for several stars. Overall, we conclude that the CaT lines are a successful metallicity indicator down to the extremely metal-poor regime and that the extremely metal-poor stars in the Sculptor dwarf galaxy are chemically more similar to their Milky Way halo equivalents than the more metal-rich population of stars. Based on observations collected at the European Organisation for Astronomical Research in the Southern Hemisphere, Chile proposal 085.D-0141.Table 3 is available in electronic form at http://www.aanda.org