Electric potential energy, or electrostatic potential energy, is a potential energy (measured in joules) that results from conservative Coulomb forces and is associated with the configuration of a particular set of point charges within a defined system. An object may have electric potential energy by virtue of two key elements: its own electric charge and its relative position to other electrically charged objects.
Lets say you have, two like charges separated by a distance. Like charges repel each other. So, both the charges repel each other. In order to explain this situation in terms of conservation of energy you need to understand that electric charge and relative position of one charge w.r.t other acts as the source of potential energy.
When one charge repels the other charge, it converts the electric potential energy stored into kinetic energy, thus separating the charges. So, law of conservation of energy hols good. Even if you consider the unlike charges, the same explanation can be given that the charges convert their potential energy into kinetic energy thus causing them to come near.