If the five-kingdom system of classification is used, the Archaea would be classified under the kingdom (d) Monera. This kingdom includes prokaryotic organisms such as bacteria and archaea. Archaea are distinct from bacteria and have unique characteristics that differentiate them from other microorganisms. They are often found in extreme environments like hot springs, deep-sea hydrothermal vents, and salt lakes.
Nitrogen-fixing organisms, on the other hand, can be found in multiple kingdoms. In the five-kingdom system, some nitrogen-fixing organisms, such as certain bacteria, would also be classified under the kingdom (d) Monera. However, it's important to note that in more modern classifications, the five-kingdom system has been expanded or replaced by more comprehensive systems, such as the three-domain system that separates life into Bacteria, Archaea, and Eukarya.