We examine a new class of CPT-even and dimension-five nonminimal interactions between fermions and photons, deprived of higher-order derivatives, yielding an electric dipole moment and magnetic dipole moment in the context of the Dirac equation. These couplings are Lorentz-violating nonminimal structures, composed of a rank-2 tensor, the electromagnetic tensor, and gamma matrices, being addressed in its axial and non-axial hermitian versions. We use the electrons anomalous magnetic and electric dipole moment measurements to reach upper bounds of 1 part in 1011 and 1016 GeV-1.