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We are motivated by recent studies in medium formed by two tunnel-coupled waveguides. One of the waveguides is manufactured from an ordinary dielectric, while the second has negative refraction. We present an investigation of the gain spectrum permitting modulation instability in the nonlinear optical coupler with a negative-index metamaterial channel whose non-linear response includes third- and fifth-order terms. The principal motivation for our analysis stems from the impact of the inevitable presence of the effective cubic–quintic nonlinearity. We emphasize the influence of higher order nonlinear terms, over the MI phenomena, and the outcome of its development achieved by using linear stability analysis. Gain spectrum investigation has been carried out for both anomalous and normal dispersion regime in the focusing and defocusing cases of nonlinearity and near-zero dispersion regime where higher order linear dispersive effects emerge. Our results show that the MI gain spectra consist of multiple spectral region which are symmetric to the zero point. Moreover, some spectra have a high cut-off frequency but a narrow spectral width, which is obviously beneficial to the generation of high-repetition-rate pulse trains. [ABSTRACT FROM AUTHOR]