State-selective single- and multiple-electron capture processes for collisions of multiply charged Kr^q+ ions (q=3-5) and Xe^q+ ions (q=3 and 4) with rare-gas atoms have been studied by means of translational energy spectroscopy, at collision energies between q and 5q keV. The collisional energy gain spectra for single-electron capture by Kr⁵⁺ from He, Ne and Ar are interpreted qualitatively in terms of the 'reaction windows', which are calculated using a multichannel Landau-Zener model. The measured energy gain spectra are in good agreement with the calculations.