Given the point $(2, 5)$ on the graph of $f(x)$, we want to find a point on the graph of $y = f(x - 3) + 1$. The given choices are $(-1, 4)$, $(-1, 6)$, $(5, 4)$, and $(5, 6)$.

1. Problem Description

Given the point $(2, 5)$ on the graph of $f(x)$, we want to find a point on the graph of $y = f(x - 3) + 1$. The given choices are $(-1, 4)$, $(-1, 6)$, $(5, 4)$, and $(5, 6)$.

2. Solution Steps

The transformation $y = f(x - 3) + 1$ involves two shifts: a horizontal shift and a vertical shift.

The horizontal shift is $x \to x - 3$, which corresponds to a shift to the right by 3 units.

The vertical shift is adding 1 to the function, which corresponds to a shift upwards by 1 unit.

So, if $(x, y)$ is a point on the graph of $f(x)$, then $(x + 3, y + 1)$ is a point on the graph of $y = f(x - 3) + 1$.

Since $(2, 5)$ is on the graph of $f(x)$, the corresponding point on the graph of $y = f(x - 3) + 1$ is $(2 + 3, 5 + 1) = (5, 6)$.

Checking the given choices, we find that $(5, 6)$ is one of the options.

3. Final Answer

(5, 6)