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PaulT5's are Pinkerton Cabinet cards. They are postcard sized black & white photos glued to a rather cheap cardboard backing. They are often seen detached from the backing. They were issued around 1910 and include some great players, including Cobb and Joe Jackson. There's also a card showing Joe McCarthy as a minor league player. They're all very tough to find -- much tougher than the T3's, but also not nearly as attractive or popular.
Don't know anything about T6 or T7.