Lattice defects in refractory metal high-entropy alloy HfNbTaTiZr are investigated using positron lifetime spectroscopy combined with coincidence Doppler broadening (CDB) spectroscopy. Annealing of HfNbTaTiZr alloy at 1000 °C results in full recovery of defects and formation of single-phase random solid solution characterized by the bulk positron lifetime of 141 ps. This value is in accordance with the theoretical estimation. Quenching of the alloy from high temperature prevents recovery of thermally equilibrium vacancies and enables to retain a high concentration of vacancies in the sample at ambient temperature. For single vacancies in the HfNbTaTiZr alloy, a characteristic positron lifetime of 212 ps is measured, which is significantly shorter than the value estimated by theoretical calculations. It indicates that there is considerable ion relaxation around vacancies. The CDB spectroscopy investigations reveal that vacancies in HfNbTaTiZr alloy are not distributed randomly but are preferentially coupled with Hf solutes.