We have a 5 hour layover at the airport in Madrid--Is there any chance to do anything other than sit and wait for our flight to be called?
The Madrid airport is huge. It has always taken me an hour or more to get from my arriving international flight, through passport control and to my connecting gate area. The airport is also well outside the city center. While 5 hours might sound like a lot of time, it really isn't enough to visit sights away from the airport. I once had a 9 hour layover, and that only allowed about 2 hours in the city center. The airport has some nice places to eat, so I suggest you grab a light meal to help pass the time. There are also some fairly comfortable sitting areas in the central areas where you can pass time before heading to the actual gate area.
Two weeks ago it took me all of 35 minutes to get from T4s to T4 to wait for my connecting flight. Most of that time was spent waiting for a train and walking from place to place - it's a big airport - but we arrived early in the morning, and there was no wait at immigration at all - no one in line in front of me. I do move fast through the airports, though.
Returning home via Madrid was a different story: there was a long line at passport control for non-EU citizens, and it moved slowly, even with multiple agents on duty. (Naturally, the agent in my line was slower than all of the other ones.) I'm sure I waited 20 minutes minimum in line. Lucky, I still had plenty of time to make my plane, which boarded late, and grab some food. But I'm sure the wait time depends in part on how busy the airport is when you arrive.
Five hours doesn't sound like a long time to me either - but if your flight arrives early (sometimes they do! Mine was 30 minutes early from the US two weeks ago), I guess you might try a quick taxi ride into Madrid and have the cab driver wait for you while you walk around somewhere for 10 minutes or something. That would probably not be cheap or something I would risk personally.