A measurement of the ratio of branching fractions of the decays B^{+}→K^{+}μ^{+}μ^{-} and B^{+}→K^{+}e^{+}e^{-} is presented. The proton-proton collision data used correspond to an integrated luminosity of 5.0 fb^{-1} recorded with the LHCb experiment at center-of-mass energies of 7, 8, and 13 TeV. For the dilepton mass-squared range 1.1<q^{2}<6.0 GeV^{2}/c^{4} the ratio of branching fractions is measured to be R_{K}=0.846_{-0.054}^{+0.060}_{-0.014}^{+0.016}, where the first uncertainty is statistical and the second systematic. This is the most precise measurement of R_{K} to date and is compatible with the standard model at the level of 2.5 standard deviations.