2015_31 Simple and elegant Part 2

Let $f\left( x \right)$ be a real valued function not identically zero such that $f\left( x+{ y }^{ n } \right) =f\left( x \right) +{ (f(y)) }^{ n }\quad \forall x,y\epsilon R$ where $n\epsilon N(n\neq 1)$ and $f^{ ' }\left( 0 \right) \ge 0$ we may get an explixity form of the function $f\left( x \right)$ .

Then the value of $f\left( 5 \right)$ is?

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