The massive Wolf-Rayet stellar system HD 5980 in the Small Magellanic Cloud entered a sudden and brief ~ 1-3 mag eruptive state in the mid-1990s. The cause of the instability is not yet understood, but mechanisms similar to those in luminous blue variables are suspected. Using a previously unreported set of spectroscopic data obtained in 1955-1967 and recently acquired optical and HST/STIS spectra, we find that (1) the brief eruptions of 1993 and 1994 occurred at the beginning of an extended (~ decades) high state of activity characterized by large emission-line intensities; (2) the level of activity is currently subsiding; and (3) another strong emission-line episode appears to have occurred between 1960 and 1965, suggesting the possibility that the long-term cyclical variability may be recurrent on a ~ 40 year timescale. These characteristics suggest the possible classification of HD 5980 as an S Doradus-type variable. The effects due to binary interactions in the system are discussed, and we tentatively suggest that the short duration and relatively hot spectral type (WN11/B1.5I) observed during maximum in the visual light curve may be attributed to these interactions.