A company has 5 TB of datasets consisting of 1 million user profiles and 10 million connections. The user profiles and connections form many-to-many relationships. The company needs an efficient way to find mutual connections up to five levels. Which solution meets these requirements?

Amazon Neptune is a fully managed graph database service. It is specifically designed to store and query highly connected datasets, making it ideal for managing relationships like social connections, recommendation engines, and fraud detection. In this scenario, user profiles and connections with many-to-many relationships are best represented as vertices (users) and edges (connections) in a graph database. Neptune's graph query languages (Gremlin or SPARQL) are highly efficient for traversing these relationships to find mutual connections up to multiple levels deep. Storing datasets in Amazon S3 and using Athena or QuickSight for SQL JOINs would be inefficient for deep, recursive relationship queries, as SQL JOINs on large datasets with many-to-many relationships become computationally expensive and slow. Amazon RDS, a relational database, would also struggle with the performance of recursive queries needed to find connections up to five levels deep, as relational databases are not optimized for graph traversals.