This paper derives two landmark predictions of quantum electrodynamics—the anomalous magnetic moment of the electron (g−2) and the Lamb shift of hydrogen—from the stochastic Coulomb field framework established in Papers 1—4 [1—4]. Both effects have the same physical origin: the zero-point radiation field (ZPF), derived in Paper 1 from the Coulomb virtual photon cloud via the Boltzmann ergodic theorem (proved in Paper 3 [3]), modifies the electron trajectory in two distinct physical situations. For the anomalous magnetic moment: the ZPF modifies the radius of the Zitterbewegung helix established in Paper 4, producing a correction to the bare g = 2 result. Integrating the ZPF spectral density SE(ω) = ℏω^3/6π^2ϵ0c^3 weighted by the time-ordering factor of the emission-reabsorption process gives the Schwinger term: ae ≡ (g − 2)/2 = α/2π ≈ 0.001 161, in agreement with the leading QED prediction and experiment. For the Lamb shift: the ZPF drives fluctuations in the electron’s position within the hydrogen atom. These fluctuations smear the electron over the Coulomb potential of the nucleus, producing an effective shift in the potential energy. Because the Laplacian of the Coulomb potential is proportional to a delta function at the origin, only s-states (l = 0) are shifted. Using the Compton cutoff ωc = mc^2/ℏ from Paper 1 and the orbital frequency as the lower cutoff, the energy shift of the 2S1/2 level is: ΔνLamb ≈ 1 040 MHz, compared with the experimental value of 1057.845 MHz—agreement to within 2% at first order. Together these results confirm that the stochastic Coulomb field framework reproduces the two most celebrated predictions of QED from purely classical foundations.