Let \(N\) be a 5-dimensional Lorentzian manifold, which satisfies the Einstein equations with an energy-momentum tensor \(T_{\alpha\beta}\). A spacelike hypersurface \(M\) of \(N\) is called asymptotically flat of order \(\tau\) if there is a compact set \(K\subset M\) such that \(M - K\) is the disjoint union of a finite number of subsets \(M_1,\dots,M_k\) (called the ``ends'' of \(M\)) each diffeomorphic to the complement of a contractible compact set in \(\mathbb{R}^4\). Under the diffeomorphism the metric of \(M_l\subset M\) is of the form \(g_{ij} =\delta_{ij} + a_{ij}\) in the standard coordinates \(\{x^i\}\) on \(\mathbb{R}^4\), where \(a_{ij}\) satisfies \(a_{ij} = O(r^{-\tau})\), \(\partial_ka_{ij} = O(r^{-\tau-1})\), \(\partial_l\partial_k a_{ij} = O(r^{-\tau-2})\). As usual the total energy \(E_l\), the total linear momentum \(p_{lk}\), and the total electromagnetic momentum \(q_{lij}\) of end \(M_l\) are defined. The Positive Mass Theorem due to R. Schoen, S. T. Yau, and E. Witten has been extended by the author [J. Math. Phys. 40, 3540-3552 (1999; Zbl 0952.83010)] to spin spacelike hypersurface in \(N\). In the present paper a further extension is given. Let \(M\subset N\) be a spacelike asymptotically flat hypersurface of order \(\tau >1\). Let \(L\) be the \(\text{Spin}^c\) structure of complex Witten-Dirac spinor bundle of \(M\) with \(U(1)\) connection \(A\), which is also asymptotically flat of order \(\tau >1\). If \(M\) satisfies a certain charged dominant energy condition, then, for each end \(M_l\) there holds an inequality for \(E_l\), involving \(p_{lk}\) and \(q_{lij}\). An analogous result is obtained for a 4-dimensional Lorentzian manifold, which satisfies the Einstein equations.