  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 results 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 black hole.
