The photoproduction of D{*}(+/-) mesons has been measured with the ZEUS detector at HERA at three different ep centre-of-mass energies, root s of 318, 251 and 225 GeV. For each data set, D{*}(+/-) mesons were required to have transverse momentum, p(T)(D){*} , and pseudo-rapidity, eta(D){*}, in the ranges 1.9 < p(T)(D){*} < 20 GeV and vertical bar eta (D{*})vertical bar < 1.6. The events were required to have a virtuality of the incoming photon, Q (2), of less than 1 GeV2. The dependence on root s was studied by normalising to the high-statistics measurement at root s = 318 GeV. This led to the cancellation of a number of systematic effects both in data and theory. Predictions from next-to-leading-order QCD describe the root s dependence of the data well.