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. Using the refined topological string formalism, we obtain the 5D partition functions for the $T_N$ theories and provide the exact AGT-W dictionary that relates them to the Toda structure constants. Using a procedure known as Higgsing, we manage to obtain the formula of Fateev and Litvinov for the Toda structure constants with one semi-degenerate primary field.