Using high-resolution Hubble Space Telescope data, we re-examine the fundamental properties (ages, masses and extinction values) of the rich star cluster population in the dwarf starburst galaxy NGC 5253. The gain in resolution compared to previous studies is of order a factor of 2 in both spatial dimensions, while our accessible wavelength range transcends previous studies by incorporation of both near-ultraviolet and near-infrared (IR) passbands. We apply spectral synthesis treatments based on two different simple stellar population model suites to our set of medium-, broad-band and H{alpha} images to gain an improved physical understanding of the IR-excess flux found for a subset of young clusters (30 of 149). With the caveat that our models are based on fully sampled stellar mass functions, the NGC 5253 cluster population is dominated by a significant number of relatively low-mass (M_cl_<~ a few x10^4^M_{sun}_) objects with ages ranging from a few x10^6^ to a few x10^7^yr, which is in excellent agreement with the starburst age of the host galaxy. The IR-excess clusters are almost all found in this young age range and have masses of up to a few x10^4^M{sun}. The IR excess in the relatively low-mass NGC 5253 clusters is most likely caused by a combination of stochastic sampling effects and colour variations due to the presence of either luminous red or pre-main-sequence stars. We also find a small number of intermediate-age (~1Gyr old), ~10^5^M{sun} clusters, as well as up to a dozen massive, ~10Gyr old globular clusters. Their presence supports the notion that NGC 5253 is a very active galaxy that has undergone multiple episodes of star cluster formation.