1. **State the problem:** We are given two functions $f(x) = x - 3$ and $g(x) = 5$. We need to evaluate the limit $$\lim_{x \to 2} 3g(x).$$ 2. **Recall the limit properties:** The limit of a constant times a function is the constant times the limit of the function, i.e., $$\lim_{x \to a} c \cdot h(x) = c \cdot \lim_{x \to a} h(x)$$ where $c$ is a constant. 3. **Evaluate the limit:** Since $g(x) = 5$ is a constant function, $$\lim_{x \to 2} g(x) = 5.$$ 4. **Apply the constant multiple rule:** $$\lim_{x \to 2} 3g(x) = 3 \cdot \lim_{x \to 2} g(x) = 3 \cdot 5 = 15.$$ **Final answer:** The limit is $15$. Therefore, the correct choice is **b. 15**.