The solvolysis rate constants of 5-dimethylamino-naphthalene-1-sulfonyl chloride ($(CH_3)_2NC_{10}H_6SO_2Cl$, 1) in 31 different solvents are well correlated with the extended Grunwald-Winstein equation, using the $N_T$ solvent nucleophilicity scale and $Y_{Cl}$ solvent ionizing scale with sensitivity values of $0.96{pm}0.09$ and $0.53{pm}0.03$ for l and m, respectively; the correlation coefficient value was 0.955. These l and m values can be considered to support an $S_N2$ reaction pathway having a transition state (TS) structure similar to that of the benzenesulfonyl chloride reaction. This interpretation is further supported by the activation parameters, i.e., relatively small positive ${Delta}H^{ eq}$ (12.0 to $15.9kcal{cdot}mol^{-1}$) and large negative ${Delta}S^{ eq}$ (-23.1 to $-36.3cal{cdot}mol^{-1}{cdot}K^{-1}$) values, and the solvent kinetic isotope effects (SKIEs, 1.34 to 1.88). Also, the selectivity values (S = 1.2 to 2.9) obtained in binary solvents are consistent with the proposed mechanism.