Final answer:
Michigan is the state that has a namesake lake, the 5th largest in the world, and the 3rd largest Great Lake.
Step-by-step explanation:
The state that houses a namesake lake, the 5th largest in the world, and the 3rd largest Great Lake is Michigan. The namesake lake refers to Lake Michigan, which is the only Great Lake that is entirely within the United States. Lake Michigan is the 5th largest lake in the world by surface area. Additionally, Michigan is also home to four other Great Lakes: Lake Superior, Lake Huron, Lake Erie, and Lake Ontario.