The present invention provides a process for purifying FV starting from human plasma or a fractionation intermediate thereof, that is simple, scalable to the industrial level and relatively inexpensive compared to the methods described in the literature to date. The invention consists of the use of two anion exchange chromatography steps, the first of which has the purpose of separating the FV from the PTC component factors, while the second has the purpose of isolating the protein of interest from the majority of plasma proteins by means of selective interaction with the weak anion exchange support used. The process developed has also had a viral inactivation step and a viral removal step included, contributing to the safety of the final product obtained, without however significantly altering the process total recovery of FV, and without necessitating the introduction of additional steps for eliminating the inactivating agents used, thanks to the order in which the various steps are conducted. The process described in the present invention also enables an FV concentrate to be obtained that is stable once frozen at −20° C.