  We consider 5d Yang-Mills theory with a compact ADE-type gauge group $G$ on
${\mathbb R}^{3,1}\times{\cal I}$, where $\cal I$ is an interval. The maximally
supersymmetric extension of this model appears after compactification on $S^1$
of 6d $\cal N$= (2,0) superconformal field theory on ${\mathbb R}^{3,1}\times
S^2_2$, where $S^2_2\cong{\cal I}\times S^1$ is a two-sphere with two
punctures. In the low-energy limit, when the length of $\cal I$ becomes small,
the 5d Yang-Mills theory reduces to a nonlinear sigma model on ${\mathbb
R}^{3,1}$ with the Lie group $G$ as its target space. It contains an infinite
tower of interacting fields whose leading term in the infrared is the
four-derivative Skyrme term. A maximally supersymmetric generalization leading
to a hyper-K\"ahler sigma-model target space is briefly discussed.
