There are two varieties of the 1865 Indian cent, the "Fancy 5" and the "Plain 5". On the Fancy 5, the top of the 5 looks "curvey", while on the Plain 5 the top of the 5 is straighter looking. Initially, it was thought that the Fancy 5 was rarer, but as the years went by, it was found that the Plain 5 is actually the rarer of the two varieties, perhaps by a factor of 2 to 1.
The 1865 Plain 5 Indian cent is rare in circulated grades, and quite rare in mint state. Full Red Gems are very rare.