1. **Problem statement:** Given that $f'(3) = 5$ and $f(3) = 5$, find the equation of the tangent line to the graph of $f$ at the point $P(3, f(3))$. 2. **Formula used:** The equation of the tangent line to a function $f$ at $x = a$ is given by: $$y = f(a) + f'(a)(x - a)$$ This formula comes from the point-slope form of a line, where the slope is the derivative $f'(a)$ and the line passes through the point $(a, f(a))$. 3. **Apply the formula:** Here, $a = 3$, $f(3) = 5$, and $f'(3) = 5$. Substitute these values: $$y = 5 + 5(x - 3)$$ 4. **Simplify the expression:** $$y = 5 + 5x - 15$$ $$y = 5x - 10$$ 5. **Interpretation:** The tangent line at $x=3$ has slope 5 and passes through $(3,5)$. Its equation is $y = 5x - 10$. **Final answer:** $$y = 5x - 10$$