  We consider supersymmetric gauge theories on $S^5$ with a negative Yang-Mills
coupling in their large $N$ limits. Using localization we compute the partition
functions and show that the pure ${\mathrm{SU}}(N)$ gauge theory descends to an
${\mathrm{SU}}(N/2)_{+N/2}\times {\mathrm{SU}}(N/2)_{-N/2}\times
{\mathrm{SU}}(2)$ Chern-Simons gauge theory as the inverse 't Hooft coupling is
taken to negative infinity for $N$ even. The Yang-Mills coupling of the
${\mathrm{SU}}(N/2)_{\pm N/2}$ is positive and infinite, while that on the
${\mathrm{SU}}(2)$ goes to zero. We also show that the odd $N$ case has
somewhat different behavior. We then study the ${\mathrm{SU}}(N/2)_{N/2}$ pure
Chern-Simons theory. While the eigenvalue density is only found numerically, we
show that its width equals $1$ in units of the inverse sphere radius, which
allows us to find the leading correction to the free energy when turning on the
Yang-Mills term. We then consider ${\mathrm{USp}}(2N)$ theories with an
antisymmetric hypermultiplet and $N_f<8$ fundamental hypermultiplets and carry
out a similar analysis. Along the way we show that the one-instanton
contribution to the partition function remains exponentially suppressed at
negative coupling for the ${\mathrm{SU}}(N)$ theories in the large $N$ limit.
