Existence, Uniqueness & Bifurcations · Medium problem

The IVP $y' = 3y^{2/3}$, $y(0) = 0$ has infinitely many solutions. One of them is $y = 0$ for $t \le c$ and $y = (t - c)^3$ for $t > c$, for some $c \ge 0$. If this solution satisfies $y(5) = 8$, find $c$.