Two stages split $c$ evenly: $f_2(5)=25/4$ (the key's $125/27$ is $f_3(5)$)

For a certain dynamic programming problem, the recurrence equation for optimal solution is found to be $f_1(c)=c$, $f_k(c)=\max_{0<x\le c}x\cdot f_{k-1}(c-x)$ for $k>1$. What is the value of $f_2(5)$?