A measurement of the branching fraction of the decay B-s(0) -> (KSKS0)-K-0 is performed using proton- proton - collision data corresponding to an integrated luminosity of 5 fb(-1) collected by the LHCb experiment between 2011 and 2016. The branching fraction is determined to be B(B-s(0) -> (KSKS0)-K-0) = [8.3 +/- 1.6(stat) +/- 0.9(syst) +/- 0.8(norm) +/- 0.3(f(s)/f(d))] x 10(-6), where the first uncertainty is statistical, the second is systematic, and the third and fourth are due to uncertainties on the branching fraction of the normalization mode B-0 -> phi K(S)(0 )and the ratio of hadronization fractions f(s)/f(d). This is the most precise measurement of this branching fraction to date. Furthermore, a measurement of the branching fraction of the decay B-s(0) -> (KSKS0)-K-0 is performed relative to that of the B-s(0) -> (KSKS0)-K-0 channel, and is found to be B(B-s(0) -> (KSKS0)-K-0)/B(B-s(0) -> (KSKS0)-K-0) = [7.5 +/- 3.1(stat) 0.5(syst) +/- 0.3(f(s)/f(d))1 x 10(-2).