  We show that extreme Myers-Perry initial data realize the unique absolute
minimum of the total mass in a physically relevant (Brill) class of maximal,
asymptotically flat, bi-axisymmetric initial data for the Einstein equations
with fixed angular momenta. As a consequence, we prove the relevant
mass-angular momentum inequality in this setting for 5-dimensional spacetimes.
That is, all data in this class satisfy the inequality $m^3\geq
\frac{27\pi}{32}\left(|\mathcal{J}_1|+|\mathcal{J}_2|\right)^2$, where $m$ and
$\mathcal{J}_i$, $i=1,2$ are the total mass and angular momenta of the
spacetime. Moreover, equality holds if and only if the initial data set is
isometric to the canonical slice of an extreme Myers-Perry black hole.
