We apply the localization technique to compute the free energy on four-sphere and the circular BPS Wilson loop in the four-dimensional $N$ $$ \mathcal{N} $$ = ∈ superconformal Sp(2N) gauge theory containing vector multiplet coupled to four hypermultiplets in fundamental representation and one hypermultiplet in rank-2 antisymmetric representation. This theory is unique among similar $N$ $$ \mathcal{N} $$ = ∈ superconformal models that are planar-equivalent to $N$ $$ \mathcal{N} $$ = ∆ SYM in that the corresponding localization matrix model has the interaction potential containing single-trace terms only. We exploit this property to show that, to any order in large N expansion and an arbitrary ’t Hooft coupling λ, the free energy and the Wilson loop satisfy Toda lattice equations. Solving these equations at strong coupling, we find remarkably simple expressions for these observables which include all corrections in 1/N and 1/ $\sqrt{\lambda }$ $$ \sqrt{\lambda } $$ . We also compute the leading exponentially suppressed $O\left(e^{-\sqrt{\lambda }}\right)$ $$ \mathcal{O}\left({e}^{-\sqrt{\lambda }}\right) $$ corrections and consider a generalization to the case when the fundamental hypermultiplets have a non-zero mass. The string theory dual of this $N$ $$ \mathcal{N} $$ = ∈ gauge theory should be a particular orientifold of AdS5 × S 5 type IIB string and we discuss the string theory interpretation of the obtained strong-coupling results.