Long-lived particles decaying to e(+/-) mu(-/+)nu, with masses between 7 and 50 GeV/c(2) and lifetimes between 2 and 50 ps, are searched for by looking at displaced vertices containing electrons and muons of opposite charges. The search is performed using 5.4 fb(-1) of pp collisions collected with the LHCb detector at a centre-of-mass energy of root s = 13 TeV. Three mechanisms of production of long-lived particles are considered: the direct pair production from quark interactions, the pair production from the decay of a Standard-Model-like Higgs boson with a mass of 125 GeV/c(2), and the charged current production from an on-shell W boson with an additional lepton. No evidence of these long-lived states is obtained and upper limits on the production cross-section times branching fraction are set on the different production modes.