For a parabola, the highest point (if it opens downward) is the vertex.

The maximum value is the $y$-coordinate of that vertex.

Type $y=a(x-1)(x-5)$ to match the x-intercepts at $x=1$ and $x=5$.

Change $a$ until the parabola’s peak aligns with the vertex shown (the axis of symmetry should be at $x=3$).

Click the vertex of the graph in Desmos and read its $y$-coordinate; that value is the maximum of $f(x)$.

From the graph, the parabola opens downward, so its maximum value occurs at the vertex.

The vertex is at $(3,4)$, so the maximum value of $f(x)$ is $4$.

Therefore, the correct choice is $4$.