wouldn't it be (0,5] because f'(0)=0 and f'(5)=10
It depends on what you interpret to be "strictly increasing".
The usual convention is that if f'(0) = 0 (i.e. the curve is stationary) at a single point, but not along an entire interval or something, then it's ok. A function that would "not" be ok in this context could be something like
\[ f(x) = \begin{cases}x^2 +1& x \in [0,\infty)\\ 1 & x \in (-\infty,0) \end{cases}\]
because the derivative is 0 along the entire interval \( (-\infty, 0)\). The reason why this is ok is because of the actual definition of monotonicity: \( x_1 < x_2 \implies f(x_1) < f(x_2) \).
Of course, in the VCE they might not do this. But personally I don't see why you wouldn't