We investigate the reach at the LHC to probe light sterile neutrinos with displaced vertices. We focus on sterile neutrinos N with masses m(N) similar to (5-30) GeV that are produced in rare decays of the standard model gauge bosons and decay inside the inner trackers of the LHC detectors. With a strategy that triggers on the prompt lepton accompanying the N displaced vertex and considers charged tracks associated with it, we show that the 13 TeV LHC with 3000/fb is able to probe active-sterile neutrino mixings down to vertical bar V-lN vertical bar(2) approximate to 10(-9), with l = e, mu, which is an improvement of up to 4 orders of magnitude when comparing with current experimental limits from trileptons and proposed lepton-jets searches. In the case when tau mixing is present, mixing angles as low as vertical bar V-tau N vertical bar(2) approximate to 10(-8) can be accessed.