Your reference to 5 million years makes me think you are referring to the desiccation of the Mediterranean Sea. The entire basin almost totally dried out in what is known as the Messinian salinity crisis, about 6.0 to 5.3 million years ago. JOIDES deep sea drilling has proved the desiccation by drilling into salt deposits and subaerial sediments, immediately overlain by deep sea sediments in what are now some of the deepest basins of the Mediterranean. It all came to an end when erosion broke through the Rif-Betic Arc, which was a land bridge between Africa and Europe. When the Atlantic broke through it produced what was probably the most spectacular waterfall in world history - and we missed it by only 5.3 million years, dammit!
Your reference mentions '4 kilometres below sea level'. The average depth of the Mediterranean is only 1.5 km, whereas the deepest part is 5.27 km. It is probable that the Nile kept the very deepest part wet even when the rest of the Mediterranean was dry, but desiccation during the late Neogene, to 4 kilometres below current sea level could very well be close to the reality. I can't think of anywhere else in the world where such deep desiccation could have occured. The Dead Sea doesn't even come close. So the reference is probably to the dry sea, rather than a dry sea.
Later additional point, I have just recalled that Bischofite, hydrated magnesium chloride, was recovered from the Eastern Mediterranean deep basin at a depth of -3580 metres. This is further proof of near total desiccation, with Mg being concentrated, by solar evaporation, to a brine at nearly 200 x the normal sea-water concentration.
