What can a first timer to Madrid see when on a 5 hour layover from the airport?
Autonomous community: Madrid
The closest points of interest to Barajas airport are Juan Carlos I Park and the IFEMA convention center. However, if you're not afraid to cut it a little close, I recommend heading straight to the Plaza Mayor (the city's historic main square).
A 5 hour layover sounds like a long wait but its not. Madrid is a big city with lots of traffic. It could take a good hour to get to the city center on the metro. I wouldn't wander too far off.