  We consider the long-standing problem of obtaining the 3-point functions of
Toda CFT. Our main tools are topological strings and the AGT-W relation between
gauge theories and 2D CFTs. In arXiv:1310.3841 we computed the partition
function of 5D $T_N$ theories on $S^4 \times S^1$ and suggested that they
should be interpreted as the three-point structure constants of q-deformed
Toda. In this paper, we provide the exact AGT-W dictionary for this relation
and rewrite the 5D $T_N$ partition function in a form that makes taking the 4D
limit possible. Thus, we obtain a prescription for the computation of the
partition function of the 4D $T_N$ theories on $S^4$, or equivalently the
undeformed 3-point Toda structure constants. Our formula, has the correct
symmetry properties, the zeros that it should and, for $N=2$, gives the known
answer for Liouville CFT.
