Ditto, last time I flew with an altimeter, it measured around 5500 ft as well. I was surprised because I thought normal air pressure is generally between the 7000-8000 ft equivalent.
UP to FL 35 it is typically 7000' above that it goes to 8000'. Flying to Shasta in my NON pressurized plane we get 2 hours at 11k before strapping on the crampons! Scott
On flights from BWI or Dulles to La Guardia, I never see the pressure rise much above 1000ft. On flights from Dulles to SEA or PDX (which stop over in MDW usually), I see the pressure go up to around 7000, sometimes a little more and sometimes a little less.
Commercial airliners are pressurized up to the max differential PSI the airframe can take. For an example, an aircraft cruising at 30,000’ with a max PSI differential of 6 will have a cabin altitude of 5,000’. The higher the differential the lower the cabin altitude (passenger comfort) while the higher the cruising altitude (fuel burn).
Cabin pressure varies by aircraft and manufacturer. I am sure there are some DOT regulations thrown in there, too.
People do get altitude sickness from flying due to the reduced cabin pressure.
The air is so dry because the air comes from bleed air, at least in jet airliners and turboprops. Bleed air is very hot (250 degrees F) and very dry air that is bled off from the intake turbines and run through a heat exchanger to cool it down. The air is heated by the process of compression, much like intake air is compressed in a turbocharger or supercharger. (Although a jet engine works more like a turbocharger than a supercharger, in that exhaust spins the rear turbine blades as it exits, thus spinning the intake turbines).
Bleed air is used to power various components on aircraft, such as the air conditioning system, windshield rain removal, starting engines, etc.
Newer aircraft are using electrical systems for air conditioning and are relying less on bleed air systems.
Either way, the air is run through condensors to eliminate moisture.