[en] In this paper, we have meticulously studied the amplitude modulation of electron-acoustic waves and the formation and properties of envelope solitons in a five-component complex plasma containing statistically kappa-distributed warm and cold electrons, kappa-distributed positrons and Boltzmann-distributed positive and negative ions. The picture considered here is very similar to solar atmosphere and planetary environments. The parametric dependence of modulational instability on kappa index, positron and electron densities, ion and reciprocal of positron temperatures has been studied in detail and the findings obtained here will be beneficial for further astrophysical investigations. (author)