Pulsars are promising targets for the first detection of continuous gravitational waves (CWs) by the LIGO-Virgo-KAGRA (LVK) Collaboration. Targeted searches leverage critical information derived from continued monitoring of pulsars related to the spin evolution, astrometry, and binary orbit. This information maximizes the probability to detect CW signals using full coherent methods. The 5-vector method is one of the three pipelines used by the LVK Collaboration for the targeted search of CWs from known pulsars. In this letter, we describe the first implementation and test of an heterodyne method to correct the orbital Doppler effect for pulsars in binary systems for the 5-vector targeted search.