The song that the blue lady (Plavalaguna) sang while Milla Jovovich was punching and kicking in the movie The Fifth Element is largely based on the "mad scene" aria Il Dolce Suono (The Sweet Dream) from Lucia Di Lammermoor. This work by Gaetano Donizetti is, according to Wikipedia, "one of the leading bel canto operas."
My favorite version so far—although I'm open to suggestions—is sung by the great Monserrat Caballé. I find her pianissimo hard to top. Certainly the version used in the movie, sung by the Albanian soprano Inva Mula-Tchako, is quite respectable, and adorned with electronic processing. Not a bad recording to have, more so if you like crossover music.
Get the soundtrack of The Fifth Element, at Amazon.com, or just the aria with Caballé from iTunes.com.
