Number Theoretic approach please!

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 \(f(5)\).

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