Five-dimensional (5D) interpolation/regularization has been routinely used for conventional P-wave (PP) pre-stack time/depth migration (PSTM/PSDM) in the common offset vector (COV) domain, particularly for merged surveys. Because the pre-stack joint inversion of PP and converted- wave (PS) data is desirable for extracting petro-physical parameters, we sought to develop a method that also handles converted-wave PSTM in a similar way as PP PSTM. We propose and compare two 5D interpolation/regularization approaches, surface-consistent 5D (SC5D) and asymptotic conversion point consistent 5D (ACPC5D). We demonstrate that 5D interpolation/regularization for converted-waves, either in the sense of surface-consistent or ACP-consistent, is an important processing step in generating PS PSTM gathers in COV domain, resulting in reduced footprint and migration artifacts. The ACP-consistent 5D interpolation/regularization method yields better amplitude-consistent imaging than surface-consistent 5D interpolation/regularization. This approach can preserve the AVO/AVAZ integrity of the PSTM gathers in the COV domain, which is desirable for pre-stack joint inversion of PP and PS data.