5. Find all functions $f: \mathbf{N}_{+} \rightarrow \mathbf{N}_{+}$, such that for all positive integers $a, b$, there exists a non-degenerate triangle with side lengths $a, f(b), f(b+f(a)-1)$ (a triangle is called non-degenerate if its three vertices are not collinear).
(France)