Final answer:
The height of the 500 mb map contour reading 557 is 5570 meters or 18,270 feet above sea level, where the '5' indicates the order of magnitude for the reading.
Step-by-step explanation:
On a 500 mb map, a height reading of 557 generally refers to the geopotential height of that specific contour. This means that the height of this contour is 5570 meters or 18,270 feet above sea level. The '5' in the beginning is significant; it tells us that we should add a zero to the number to obtain the full geopotential height. This is a common practice in reading weather maps or upper-air charts, where the contour value is presented in decameters (tens of meters) for simplicity and the leading digit is understood to provide the order of magnitude.