  The article studies the Fifth Painlev\'e equation and of the nonlinear Stokes
phenomenon at its irregular singularity at infinity from the point of view of
confluence from the Sixth Painlev\'e equation. This approach is developped
separately on both sides of the Riemann-Hilbert correspondance. On the side of
the nonlinear Painlev\'e-Okamoto foliation the relation between the nonlinear
monodromy group of Painlev\'e VI and the "nonlinear wild monodromy pseudogroup"
of Painlev\'e V (that is the pseudogroup generated by nonlinear monodromy,
nonlinear Stokes operators and nonlinear exponential torus) is explained in
detail. On the side of the corresponding linear isomonodromic problem, the
"wild" character variety (the space of the linear monodromy and Stokes data)
associated to Painlev\'e V is constructed through a birational transformation
from the character variety (the space of the linear monodromy data) associated
to Painlev\'e VI. This allows to transport the known description of the action
of the nonlinear monodromy of Painlev\'e VI on its character variety to that of
Painlev\'e V, and to provide explicit formulas for the action of the "nonlinear
wild monodromy" of Painlev\'e V on its character variety.
