Denote by $$\mathbb N$$ the set of all positive integers. A function $$f : \mathbb N \rightarrow \mathbb N$$ is such that for all positive integers $$m$$ and $$n$$, the integer $$f(m) + f(n) - mn$$ is non-zero and divides $$mf(m) + nf(n)$$.
Then find the value of $$f(5)$$.