  The AdS_5 superalgebra PSU(2,2|4) has an infinite dimensional extension,
which we denote by hs(2,2|4). We show that the gauging of hs(2,2|4) gives rise
to a spectrum of physical massless fields which coincides with the symmetric
tensor product of two AdS_5 spin-1 doubletons (i.e. the N=4 SYM multiplets
living on the boundary of AdS_5). This product decomposes into levels
\ell=0,1,2,..,\infty of massless supermultiplets of PSU(2,2|4). In particular,
the D=5, N=8 supergravity multiplet arises at level \ell=0. In addition to a
master gauge field, we construct a master scalar field containing the s=0,1/2
fields, the anti-symmetric tensor field of the gauged supergravity and its
higher spin analogs. We define the linearized constraints and obtain the
linearized field equations of the full spectrum, including those of D=5,N=8
gauged supergravity and in particular the self-duality equations for the 2-form
potentials of the gauged supergravity (forming a 6-plet of SU(4)), and their
higher spin cousins with s=2,3,...,\infty.
