  In this letter, we examine a new class of CPT-even nonminimal interactions,
between fermions and photons, deprived of higher order derivatives, that yields
electric dipole moment (EDM) and magnetic dipole moment (MDM) in the context of
the Dirac equation. The couplings are dimension-five CPT-even and
Lorentz-violating nonminimal structures, composed of a rank-2 tensor,
$T_{\mu\nu}$, the electromagnetic tensor, and gamma matrices, being addressed
in its axial and non-axial Hermitian versions, and also comprising general
possibilities. We then use the electron's anomalous magnetic dipole moment and
electron electric dipole moment measurements to reach upper bounds of $1$ part
in $10^{20}$ and $10^{25}$ (eV )$^{-1}$.
