We report the results of the first ∼ 4 years of spectroscopic and photometric monitoring of the Type IIn supernova SN 2015da (aka PSN J13522411+3941286, or iPTF16tu). The supernova exploded in the nearby spiral galaxy NGC 5337, in a relatively highly extinguished environment. SN 2015da shows prominent Balmer lines in emission with narrow components at all times and a slow rise to maximum. In addition, early observations performed by amateur astronomers give a very well-constrained explosion epoch. The observables are consistent with continuous interaction between the supernova ejecta and a dense and extended H-rich circumstellar medium. This is likely the mechanism powering the light curve, as confirmed by the analysis of the pseudo bolometric light curve, which gives a total radiated energy 10 51 erg. Modeling the light curve in the context of a supernova shock breakout through a dense circumstellar medium allowed us to infer the mass of the pre-existing gas to be > 8.2 M , with an extreme mass-loss rate for the progenitor star 0.4 − 0.8 M yr −1 , suggesting that most of the circumstellar gas was produced during multiple eruptive events. Near-and mid-infrared observations reveal a flux excess in these domains, similar to those observed in SN 2010jl and other interacting transients, likely due to pre-existing radiatively-heated dust surrounding the supernova. By modeling the infrared excess, we infer a mass 0.4 × 10 −3 M for the dust.