If the Earth's atmosphere does have five layers, then the middle one – as its name implies – is the Mesosphere.
According to NASA however, "the Earth's atmosphere has four primary layers: the troposphere, stratosphere, mesosphere, and thermosphere."
Wikipedia starts off agreeing with (if not quoting) NASA, but then seems to contradict itself: "the atmosphere has four primary layers, which are the troposphere, stratosphere, mesosphere, and thermosphere. From highest to lowest, the five main layers are: [Exosphere, Thermosphere, Mesosphere, Stratosphere, Troposphere]."
The extra (fifth) layer – the one that's (apparently) a main layer but not a primary layer – is the Exosphere. According to Wikipedia, the atoms and molecules in the Exosphere "are so far apart that they can travel hundreds of kilometers without colliding with one another. Thus, the exosphere no longer behaves like a gas, and the particles constantly escape into space."
The Exosphere is where most man–made satellites orbit the Earth.
The question does echo Wikipedia's terminology, mentioning "the five main layers" rather than the "four primary layers". But I have my doubts about how scientific these terms actually are. NASA doesn't seem to mention "main layers" – or indeed the Exosphere.
The waters are further muddied if you mention the Ionosphere. This includes the Mesosphere, Thermosphere, and parts of the Exosphere. According to Wikipedia, it "forms the inner edge of the magnetosphere". Yet another layer!
At the end of the day, I can't really argue with the question as it stands because (as I said at the top) if the atmosphere does have five layers, the middle one is the Mesosphere. I'd just like to know who it was that decided there were five main layers!
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