Despite the lack of reproducible experimental confirmation, group-V elements have been considered as possible sources of p-type doping in ZnO in the form of simple and complex defects. Using ab initio calculations, based on state-of-the-art hybrid exchange-correlation functional, we study a wide range of defects and defect complexes related with N, P, As, and Sb impurities. We show that none of the candidates for p-type doping can be considered a good source of holes in the valence band due to deep acceptor levels and low formation energies of compensating donor defects. In addition, we discuss the stability of complexes in different regimes.