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Over the past 40 years, the massive LBV/WR system HD 5980 in the Small Magellanic Cloud has undergone a long-term S Doradus type variability cycle and two brief and violent eruptions in 1993 and 1994. In this paper we analyze a collection of UV and optical spectra obtained between 1979 and 2009 and perform CMFGEN model fits to spectra of 1994, 2000, 2002 and 2009. The results are as follows: a) The long term S Dor-type variability is associated with changes of the hydrostatic radius; b) The 1994 eruption involved changes in its bolometric luminosity and wind structure; c) the emission-line strength, the wind velocity and the continuum luminosity underwent correlated variations in the sense that a decreasing V$_\infty$ is associated with increasing emission line and continuum levels; and d) The spectrum of the third star in the system ({\it Star C}) is well-fit by a T$_{eff}$=32 K model atmosphere with SMC chemical abundances. For all epochs, the wind of the erupting star is optically thick at the sonic point and is thus driven mainly by the continuum opacity. We speculate that the wind switches between two stable regimes driven by the "hot" (during the eruption) and the "cool" (post-eruption) iron opacity bumps as defined by Lamers & Nugis (2002) and Gr��fener and Hamann (2008), and thus the wind may undergo a bi-stability jump of a different nature from that which occurs in OB-stars., 55 pages, 17 figures, 6 tables