  In this letter we present a scan for new vacua within consistent truncations
of eleven/ten-dimensional supergravity down to five dimensions that preserve $N
= 2$ supersymmetry, after their complete classification in arXiv:2112.03931. We
first make explicit the link between the equations of exceptional
Sasaki-Einstein backgrounds in arXiv:1602.02158 and the standard BPS equations
for $5d$ $N = 2$ of arXiv:1601.00482. This derivation allows us to expedite a
scan for vacua preserving $N = 2$ supersymmetry within the framework used for
the classification presented in arXiv:2112.03931.
