We present a sample of 21 hydrogen-free superluminous supernovae (SLSNe-I) and one hydrogen-rich SLSN (SLSN-II) detected during the five-year Dark Energy Survey (DES). These SNe, located in the redshift range 0.220 > z > 1.998, represent the largest homogeneously selected sample of SLSN events at high redshift. We present the observed g, r, i, z light curves for these SNe, which we interpolate using Gaussian processes. The resulting light curves are analysed to determine the luminosity function of SLSNe-I, and their evolutionary time-scales. The DES SLSN-I sample significantly broadens the distribution of SLSN-I light-curve properties when combined with existing samples from the literature. We fit a magnetar model to our SLSNe, and find that this model alone is unable to replicate the behaviour of many of the bolometric light curves. We search the DES SLSN-I light curves for the presence of initial peaks prior to the main light-curve peak. Using a shock breakout model, our Monte Carlo search finds that 3 of our 14 events with pre-max data display such initial peaks. However, 10 events show no evidence for such peaks, in some cases down to an absolute magnitude of >−16, suggesting that such features are not ubiquitous to all SLSN-I events. We also identify a red pre-peak feature within the light curve of one SLSN, which is comparable to that observed within SN2018bsz.