When you say five buttons, does LBM, RBM and MouseWheel Down count? As in two extra buttons? Because then I can recommend QPAD 5K. It has a five-finger grip, as opposed to the four-finger grip that most mice has. That way your pinkie won't get in the way of the mouse.
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Yes, LMB, RMB, MW , and a few side buttons. Something kind of like this, but I'm not sure I need THAT many buttons, just more than 3 and at least 5.