  This paper concerns the formation of singularities in the classical
$(5+1)$-dimensional, co-rotational Skyrme model. While it is well established
that blowup is excluded in $(3+1)$-dimensions, nothing appears to be known in
the higher dimensional case. We prove that the model, in the so-called strong
field limit, admits an explicit self-similar solution which is asymptotically
stable within backwards light cones. From a technical point of view, the main
obstacle to this result is the presence of derivative nonlinearities in the
corresponding evolution equation. These introduce first order terms in the
linearized flow which render standard techniques useless. We demonstrate how
this problem can be bypassed by using structural properties of the Skyrme
model.
