Summary: We describe a one-parameter family of new holographic RG flows that start from \(\mathrm{AdS}_4\times S^7\) and go to \(\widehat{AdS}_5 \times\mathcal B_6\), where \(\mathcal B_6\) is conformal to a Kähler manifold and \(\widehat{\mathrm{AdS}}_5\) is Poincaré \(\mathrm{AdS}_5\) with one spatial direction compactified and fibered over \(\mathcal B_6\). The new solutions ‘flow up dimensions,’ going from the \((2+1)\)-dimensional conformal field theory on M2 branes in the UV to a \((3+1)\)-dimensional field theory on intersecting M5 branes in the infra-red. The M2 branes completely polarize into M5 branes along the flow and the Poincaré sections of the \(\widehat{\mathrm{AdS}}_5\) are the \((3+1)\)-dimensional common intersection of the M5 branes. The emergence of the extra dimension in the infra-red suggests a new strongly-coupled phase of the M2 brane and ABJM theories in which charged solitons are becoming massless. The flow solution is first analyzed by finding a four-dimensional \(\mathcal N=2\) supersymmetric flow in \(\mathcal N=8\) gauged supergravity. This is then generalized to a one parameter family of non-supersymmetric flows. The infra-red limit of the solutions appears to be quite singular in four dimensions but the uplift to eleven-dimensional supergravity is remarkable and regular (up to orbifolding). Our construction is a non-trivial application of the recently derived uplift formulae for fluxes, going well beyond the earlier constructions of stationary points solutions. The eleven-dimensional supersymmetry is also analyzed and shows how, for the supersymmetric flow, the M2-brane supersymmetry in the UV is polarized entirely into M5-brane supersymmetry in the infra-red.