Answer :

Layers of the Earth's atmosphere
1. Troposphere -- clouds and weather occur here
2. Stratosphere -- contains the ozone layer which protects from Sun UV radiation
3. Mesosphere -- shooting stars usually burn up here
4. Thermosphere -- gases here move very fast, making it measure as hot but feel cold. The Hubble Telescope orbits at this altitutde.
5. Exosphere -- the region beyond the thermosphere, i.e., outer space.

The ionosphere is in the thermosphere and part of the exosphere, where air is ionized by UV light.

As for layers of the Earth as in beneath the Earth...
1. Crust -- solid rock @ surface/earth. this & upper mantle make the lithosphere
2. Upper mantle -- solid rock below the tectonic plates in the crust.
3. Mantle -- solid magma which flows due to convection currents, specifically in the asthenosphere near the upper mantle.
4. Outer core -- liquid, less dense metal towards the center. s-waves can't go thru.
5. Inner core -- solid metal, most dense and hottest of all.

It's hard to exactly decide what comes fifth... Here's the possibilities:
crust, upper mantle, asthenosphere, lower mantle, outer core, inner core
crust and upper mantle can combine to make lithosphere...
asthenosphere can be left out as part of the upper mantle
lower mantle and upper mantle can combine to make the mantle...
it's not likely that the cores aren't mentioned in two parts, though...
Just pick inner core and roll with it I guess. Be prepared to debate!