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Aims. This work aims at constraining the masses and separations of potential substellar companions to five accelerating stars (HIP 1481, HIP 88399, HIP 96334, HIP 30314 and HIP 116063) using multiple data sets acquired with different techniques. Methods. Our targets were originally observed as part of the SPHERE/SHINE survey, and radial velocity (RV) archive data were also available for four of the five objects. No companions were originally detected in any of these data sets, but the presence of significant proper motion anomalies (PMa) for all the stars strongly suggested the presence of a companion. Combining the information from the PMa with the limits derived from the RV and SPHERE data, we were able to put constraints on the characteristics of the unseen companions. Results. Our analysis led to relatively strong constraints for both HIP 1481 and HIP 88399, narrowing down the companion masses to 2-5 M_Jup and 3-5 M_Jup and separations within 2-15 au and 3-9 au, respectively. Because of the large age uncertainties for HIP 96334, the poor observing conditions for the SPHERE epochs of HIP 30314 and the lack of RV data for HIP 116063, the results for these targets were not as well defined, but we were still able to constrain the properties of the putative companions within a reasonable confidence level. Conclusions. For all five targets, our analysis has revealed that the companions responsible for the PMa signal would be well within reach for future instruments planned for the ELT (e.g., MICADO), which would easily achieve the required contrast and angular resolution. Our results therefore represent yet another confirmation of the power of multi-technique approaches for both the discovery and characterisation of planetary systems.