@PercyButtons3 @DailyEpsilon

max (S_u) = f(u) implies
2uv - f(v) \leq f(u)
or
f(u) + f(v) \geq 2uv
With v = u we get f(u) \geq u^2

Now,
f(u) = max (S_u)
means
f(u) = \max_v ( 2uv - f(v) ) \leq \max_v ( 2uv - v^2) = (2 u u - u^2) = u^2

We have bounded f(u) by u^2 on both sides, which means f(u) = u^2 and f(5) = 25.