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We study higher order corrections to extremal black holes/black
string in five dimensions. These higher order corrections are due
to supersymmetric completion of $R^2$ term in five dimensions. By
making use of the result we extend the notion of very special
geometry when higher derivative terms are also taken into account.
This can be used to make a connection between total bundle space
of near horizon wrapped M2's and wrapped M5's in the presence of
higher order corrections. We also show how the corrected geometry
removes the singularity of a small back holes.
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