1. **State the problem:** Solve the inequality $x^2 - 5x + 6 < 0$. 2. **Recall the formula:** This is a quadratic inequality. We first find the roots of the quadratic equation $x^2 - 5x + 6 = 0$ using factorization or the quadratic formula. 3. **Factor the quadratic:** $$x^2 - 5x + 6 = (x - 2)(x - 3)$$ 4. **Find the roots:** Set each factor equal to zero: $$x - 2 = 0 \Rightarrow x = 2$$ $$x - 3 = 0 \Rightarrow x = 3$$ 5. **Analyze the inequality:** The quadratic opens upwards (coefficient of $x^2$ is positive), so the parabola is positive outside the roots and negative between them. 6. **Solution:** The inequality $x^2 - 5x + 6 < 0$ holds for values of $x$ between the roots: $$2 < x < 3$$ **Final answer:** The solution set is $\boxed{(2, 3)}$.