Prototyping three-dimensional (3D) printed electronics via material extrusion (MEX) has become popular in recent years with the increased availability of commercial conductive filaments. However, the current planar 3D printing method of layer upon layer construction shows clear challenges in extruding conductive traces for inclining surfaces. This inherent limitation of planar 3D printing restricts the design freedom of 3D printed electrically conductive objects with conductive filaments based on Polylactic Acid (PLA). To overcome this limitation of planar 3D printing, this paper describes a novel method of employing a multi-material 5-axis 3D printer to extrude conductive PLA in curved layers. The paper characterises changes in the resistivity of printed traces for angles of incline and curvatures using two commercial conductive PLA filaments. Conductive traces were printed via a custom-built desktop 5-axis 3D printer and a conventional multi-material MEX 3D printer. We found that 3D printing following a conformal approach can reduce the resistivity of the vertical conductive trace by more than 9 times. The paper concludes by successfully fabricating complex conductive patterns onto free-form doubly curved substrates.