  We show that little string theory on S^5 can be obtained as double-scaling
limits of the maximally supersymmetric Yang-Mills theories on RxS^2 and
RxS^3/Z_k. By matching the gauge theory parameters with those in the gravity
duals found by Lin and Maldacena, we determine the limits in the gauge theories
that correspond to decoupling of NS5-brane degrees of freedom. We find that for
the theory on RxS^2, the 't Hooft coupling must be scaled like ln^3(N), and on
RxS^3/Z_k, like ln^2(N). Accordingly, taking these limits in these field
theories gives Lagrangian definitions of little string theory on S^5.
