The production cross-sections of Υ mesons, namely Υ(1S), Υ(2S) and Υ(3S), in pp collisions at √s ​ = 5 TeV are measured with a data sample corresponding to an integrated luminosity of 9.13 ± 0.18 pb−1−1 collected by the LHCb detector. The Υ mesons are reconstructed in the decay mode Υ → μ++μ−−. Double differential cross-sections times branching fractions, as functions of the transverse momentum pTT​ and the rapidity y of the Υ mesons, are measured in the range pTT​< 20 GeV/c and 2.0 < y < 4.5. The results integrated over these pTT​ and y ranges areσ(Y(1S))×B(Y(1S)→μ+μ−)=2101±33±83 pb,σ(Y(2S))×B(Y(2S)→μ+μ−)=526±20±21 pb,σ(Y(3S))×B(Y(3S)→μ+μ−)=242±16±10 pb,σ(Y(1S))×B(Y(1S)→μ+μ−)=2101±33±83 pb,σ(Y(2S))×B(Y(2S)→μ+μ−)=526±20±21 pb,σ(Y(3S))×B(Y(3S)→μ+μ−)=242±16±10 pb,where the first uncertainties are statistical and the second are systematic. The ratios of cross-sections between measurements of two different Υ states and between measurements at different centre-of-mass energies are determined. The nuclear modification factor of Υ(1S) at √s ​ = 5 TeV is updated as well using the directly measured cross-section results from this analysis. [graphic not available: see fulltext]