  In this article we use 5-brane junctions to study the 5D T_N SCFTs
corresponding to the 5D N=1 uplift of the 4D N=2 strongly coupled gauge
theories, which are obtained by compactifying N M5 branes on a sphere with
three full punctures. Even though these theories have no Lagrangian
description, by using the 5-brane junctions proposed by Benini, Benvenuti and
Tachikawa, we are able to derive their Seiberg-Witten curves and Nekrasov
partition functions. We cross-check our results with the 5D superconformal
index proposed by Kim, Kim and Lee. Through the AGTW correspondence, we discuss
the relations between 5D superconformal indices and n-point functions of the
q-deformed W_N Toda theories.
