  Massive type IIA supergravity admits a warped AdS_6 x S^4 vacuum solution,
which is expected to be dual to an N=2, D=5 super-conformal Yang-Mills theory.
We study solutions for strings rotating or spinning in this background. The
warp factor plays no essential role when the string spins in the AdS_6,
implying a commonality in the leading Regge trajectories between the D=4 and
D=5 super-conformal field theories. The warp factor does, however, become
important when the string rotates in the S^4, in particular for long strings,
which have the the relation E- 3J/2=c_1 + c_2/J^5+..., where the angular
momentum J is large. This relation is qualitatively different from that for
long strings in the AdS_5 x S^5 background. We also study Penrose limits of the
AdS_6 x S^4 solution, one of which gives rise to a free massive string theory
with time-dependent masses.
