The Hamiltonian for triatomic and tetraatomic systems in row-orthonormal hyperspherical coordinates has been derived previously. However, for pentaatomic systems this derivation requires nontrivial generalizations. These are presented in this paper, together with the corresponding Hamiltonian. Each of the twelve operators that contribute to this Hamiltonian is kinematic-rotation invariant. As for the triatomic and tetraatomic cases, these pentaatomic demcocratic coordinates are particularly well suited for calculations of reactive scattering in five atom systems.