Partially and fully fluorinated olefins are a class of compounds with relatively short atmospheric lifetimes and low 100-year global warming potentials, compared to their saturated predecessors, which are used or considered as refrigerants, propellants, solvents, and other end-uses. The cyclic unsaturated compounds c-C5F8 and c-C5HF7 are currently under consideration as etching agents for the semiconductor industry. In this study, we expand on our previous work on the reaction of the OH radical with c-C5F8 and c-C5HF7 and report the rate coefficients, k, for the gas-phase reaction of the Cl atom with c-C5F8 and c-C5HF7 over a range of temperature (245-367 K) and pressure (100-200 Torr of He or N2 and 0 to 4.8 Torr O2) using a pulsed laser photolysis-resonance fluorescence (PLP-RF) technique. In addition, a relative rate (RR) technique, employing multiple reference compounds, was used to study the Cl atom reactions at 296 K, 100 and 630 Torr (N2 or air) total pressure. Reaction rate coefficients, k1, of the Cl atom reaction with c-C5F8 were found to be independent of pressure, over the pressure range used in this work, with k1(296 K), derived as an average of results from the PLP-RF and RR techniques being (1.07 ± 0.02) × 10-12 cm3 molecule-1 s-1 and k1(T) = (7.76 ± 0.73) × 10-13 × (exp[(98 ± 26)/T]) cm3 molecule-1 s-1, where the quoted error limits represent the 2σ data precision. Rate coefficients, k2, for the Cl atom + c-C5HF7 reaction were measured to be k2(296 K) = (4.61 ± 0.10) × 10-12 cm3 molecule-1 s-1 and k2(T) = (7.42 ± 0.89) × 10-13 × (exp[(540 ± 32)/T]) cm3 molecule-1 s-1. The Cl atom temporal profiles, observed with the PLP-RF technique, indicate that the Cl atom with c-C5F8 and c-C5HF7 reactions lead to adduct formation. The equilibrium constants for adduct formation were derived in this work, and a second-law analysis was used to obtain ΔH and ΔS values of -18.5 ± 0.4 kcal mol-1, -30.9 ± 1.2 cal K-1 mol-1, and -13.9 ± 0.5 kcal mol-1, -27.6 ± 1.1 cal K-1 mol-1 for the c-C5F8 and c-C5HF7 reactions, respectively. The Cl-initiated degradation of c-C5F8 and c-C5HF7 in the presence of O2 was studied and stable products were identified via infrared spectroscopy using experimental or theoretically derived spectra from our previous OH reaction work. For c-C5F8, FC(O)CF2CF2CF2C(O)F and FC(O)C(O)F were observed with molar yields of 0.80 and 0.10, respectively. For c-C5HF7, we observed the formation of HC(O)CF2CF2CF2C(O)F and HC(O)C(O)F with a combined molar yield of 0.72. Carbonyl difluoride, F2CO, was also a major product in the decomposition of c-C5F8 and c-C5HF7. The oxidation mechanism of the Cl-initiated degradation of c-C5F8 and c-C5HF7 is discussed. Based on the combined findings from this and our previous work, the atmospheric implications from the use of c-C5F8 and c-C5HF7 are presented.