  Let $G$ be a compact Lie group acting effectively by isometries on a compact
Riemannian manifold $M$ with nonempty fixed point set $Fix(M,G)$. We say that
the action is \emph{fixed point homogeneous} if $G$ acts transitively on a
normal sphere to some component of $Fix(M,G)$, equivalently, if $Fix(M,G)$ has
codimension one in the orbit space of the action. We classify up to
diffeomorphism closed, simply connected 5-manifolds with nonnegative sectional
curvature and an effective fixed point homogeneous isometric action of a
compact Lie group.
