  We look for critical points with U(2) residual symmetry in 5-dimensional
maximally supersymmetric gauged supergravity, by varying the embedding tensor,
rather than directly minimizing the scalar potential. We recover all previously
known vacua and we find four new vacua, with different gauge groups and
cosmological constants. We provide the first example of a maximal supergravity
model in $D \geq 4$ having critical points with both positive and vanishing
cosmological constant. For each vacuum we also compute the full mass spectrum.
All results are analytic.
