This research is focused on the 4f-5d transitions in Ce(3+) centers doped into tetragonal β-SrAlF(5) single crystals belonging to the I4(1)/a space group. The presence of four non-equivalent Sr(2+) sites in this compound leads to the appearance of three spectroscopically non-equivalent Ce(3+) luminescence centers, which can be well distinguished using a time-resolved laser spectroscopy technique. All 4f-5d transitions have slightly varying excitation and emission energies with characteristic probabilities resulting in several decay times that can be determined experimentally. One of these centers experiences strong perturbation due to a defect nearby, probably the O(2-) impurity ion substituting for the F(-) ion and acting as a charge compensator as well. Identification of these photoluminescence centers is performed using crystal field calculations. The crystal field parameters are calculated for two identified centers using the structural data for SrAlF(5); diagonalization of the crystal field Hamiltonian results in obtaining the splitting of the Ce(3+) 5d states. This method allows 'regular' unperturbed Ce(3+) centers with selected Sr(2+) sites to be assigned.