The KLL dielectronic recombination (DR) process of C5+ ion embedded in Debye plasmas is investigated using the multiconfiguration Dirac-Fock method with the Debye-Hückel model potential. The resonance energies, radiative and Auger rates as well as DR cross sections are obtained for a large range of Debye screening parameters to explore the influences of the plasma screening on the KLL DR process of C5+ ion. It is found that the total radiative rates and Auger rates of the intermediate states both decrease monotonically with increasing the plasma screening, except the Auger rate for the transition 2p2 1S → 1s that changes nonmonotonically due to such screening imposed on the interaction between the configurations 1s and 2s in C5+ ion. Moreover, for the KLL DR process, blueshift and redshift phenomena are observed for the resonance energies, which originates from the dynamic variations of the energy levels of C4+ and C5+ ions in the Debye plasma. The magnitudes of the DR cross section decrease slightly when the Debye-screening effects are not so strong.