  In this paper, we consider the heat flow for Yang-Mills connections on
$\mathbb{R}^5 \times SO(5)$. In the $SO(5)-$equivariant setting, the Yang-Mills
heat equation reduces to a single semilinear reaction-diffusion equation for
which an explicit self-similar blowup solution was found by Weinkove
\cite{Wei04}. We prove the nonlinear asymptotic stability of this solution
under small perturbations. In particular, we show that there exists an open set
of initial conditions in a suitable topology such that the corresponding
solutions blow up in finite time and converge to a non-trivial self-similar
blowup profile on an unbounded domain. Convergence is obtained in suitable
Sobolev norms and in $L^{\infty}$.
