1. **State the problem:** Find the limit $$\lim_{x \to 5} (x^2 - 3x)$$. 2. **Recall the limit rule for polynomials:** The limit of a polynomial function as $x$ approaches a value is simply the value of the polynomial evaluated at that point. 3. **Evaluate the expression at $x=5$:** $$5^2 - 3 \times 5 = 25 - 15 = 10$$ 4. **Conclusion:** The limit is $$10$$ because the polynomial is continuous at $x=5$. Therefore, $$\lim_{x \to 5} (x^2 - 3x) = 10$$.