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The correct choice refers to a Great Great Grand Master Key System, which is indeed defined as possessing five or more levels of keying. This extensive hierarchical structure allows for a high degree of access control, where keys can be designed to operate multiple lock combinations at various levels.

In a Great Great Grand Master Key System, the hierarchy typically includes individual keys for specific locks, master keys that can open several of those locks, grand master keys that operate groups of master keys, and further levels creating even more comprehensive access controls. This configuration is often used in large facilities or organizations where distinct access needs are a priority, enabling secured entry while managing a complex network of keys.

Other key systems like the Master Key System or the Grand Master Key System consist of fewer access levels, typically three or four, which do not meet the criteria defined in the question. Therefore, the Great Great Grand Master Key System stands out as the correct answer due to its unique capability of offering five or more keying levels.