In this paper, we discuss the problem of derivation of kinetic equations from the theory of weak turbulence for the quintic Schrödinger equation. We study the quintic Schrödinger equation on L\mathbb{T} , with L\gg 1 and with a non-linearity of size \varepsilon\ll 1 . We consider the correlations f(T) of the Fourier coefficients of the solution at times t=T\varepsilon^{-2} when \varepsilon\rightarrow 0 and L\rightarrow\infty . Our results can be summed up in the following way: there exists a regime for \varepsilon and L such that for T dyadic, f(T) has the form expected from the Physics literature for kinetic regimes, but such that f has an infinite number of discontinuity points. This discontinuity appears in the context of finite-box effects.