Summary: Applying string dualities to F-theory, we obtain various \([p, q]\)-branes whose constituents are standard branes of codimension two and exotic branes. We construct junctions of the exotic five-branes and their Hanany-Witten transitions associated with those in F-theory. In this procedure, we understand the monodromy of the single \(5^2_2\)-brane. We also find the objects which are sensitive to the branch cut of the \(5^2_2\)-brane. Considering the web of branes in the presence of multiple exotic five-branes analogous to the web of five-branes with multiple seven-branes, we obtain novel brane constructions for \(\mathrm{SU}(2)\) gauge theories with \(n\) flavors and their superconformal limit with enhanced \(E_{n+1}\) symmetry in five, four, and three dimensions. Hence, adapting the techniques of the seven-branes to the exotic branes, we will be able to construct F-theories in diverse dimensions.