Using density functional theory (DFT), we characterize the interaction of screw dislocations with interstitial impurities, in particular oxygen, nitrogen and carbon, in the HfNbTaTiZr alloy of body-centered cubic (BCC) structure. Considering different configurations representative of the disordered solid solution alloy, we evidence a noticeable core spreading of the screw dislocation whether with or without solute, associated with a wide range in dislocation-solute interaction energy, which is found to be mainly attractive for the three investigated impurities. This interaction energy is shown to be highly influenced by the type of the metal atoms in the neighbourhood of the solute. Notably the more BCC elements are present around the solute (either Nb or Ta), the more repulsive this interaction is.