The origin of the enhanced abundances of both s- and r-process elements observed in a subclass of Carbon-Enhanced Metal-Poor (CEMP) stars, i.e., CEMP-r/s stars, still remains poorly understood. The i-process nucleosynthesis has been suggested as one of the most promising mechanisms for the origin of these stars. To better understand the chemical signatures and formation mechanism(s) of five previously claimed potential CH star candidates HE 0017+0055, HE 2144-1832, HE 2339-0837, HD 145777 and CD-27 14351 through a detailed systematic follow-up spectroscopic study based on high-resolution spectra. The stellar atmospheric parameters, the effective temperature T_eff_, the microturbulent velocity {zeta}, the surface gravity logg, and the metallicity [Fe/H] are derived from local thermodynamic equilibrium analyses using model atmospheres. Elemental abundances of C, N, {alpha}-elements, iron-peak elements and several neutron-capture elements are estimated using the equivalent width measurement technique as well as spectrum synthesis calculations in some cases. In the context of the double enhancement observed in four of the programme stars, we have critically examined if the literature i-process model yields ([X/Fe]) of heavy elements can explain the observed abundance distribution. The estimated metallicity [Fe/H] of the programme stars ranges from -1.63 to -2.74. All the five stars show enhanced abundance for Ba and four of them exhibit enhanced abundance for Eu. Based on our analysis, HE 0017+0055, HE 2144-1832 and HE 2339-0837 are found to be CEMP-r/s stars, whereas HD 145777 and CD-27 14351 show characteristic properties of CEMP-s stars. From a detailed analysis of different classifiers of CEMP stars, we have identified the one which best describes the CEMP-s and CEMP-r/s stars. We found that for both CEMP-s and CEMP-r/s stars, [Ba/Eu] and [La/Eu] exhibit positive values and [Ba/Fe]>=1.0. However, CEMP-r/s stars satisfy [Eu/Fe]>=1.0, 0.0<=[Ba/Eu]<=1.0 and/or 0.0<=[La/Eu]<=0.7. CEMP-s stars normally show [Eu/Fe]<1.0 with [Ba/Eu]>0.0 and/or [La/Eu]>0.5. If [Eu/Fe]~>=1.0, then the condition on [Ba/Eu] and/or [La/Eu] for a star to be a CEMP-s star is [Ba/Eu]>1.0 and/or [La/Eu]>0.7. Using a large sample of similar stars from the literature we have examined if [hs/ls] alone can be used as a classifier, and if there are any limiting values for [hs/ls] ratio that can be used to distinguish CEMP-s and CEMP-r/s stars. In spite of peaking at different values of [hs/ls], CEMP-s and CEMP-r/s stars show an overlap in the range 0.0<[hs/ls]<1.5 ,and hence, this ratio cannot be used to distinguish CEMP-s and CEMP-r/s stars. We have noticed a similar overlap in the case of [Sr/Ba] ratio as well, in the range -1.6<[Sr/Ba]<-0.5 and hence, this ratio also cannot be used to separate the two subclasses, CEMP-s and CEMP-r/s.