1. **State the problem:** Simplify the expression $$(\sqrt{x} + 5)(\sqrt{x} - 3)$$. 2. **Recall the formula:** This is a product of two binomials, which can be expanded using the distributive property (FOIL method): $$ (a + b)(c + d) = ac + ad + bc + bd $$ 3. **Apply the formula:** Here, $a = \sqrt{x}$, $b = 5$, $c = \sqrt{x}$, and $d = -3$. $$ (\sqrt{x} + 5)(\sqrt{x} - 3) = \sqrt{x} \cdot \sqrt{x} + \sqrt{x} \cdot (-3) + 5 \cdot \sqrt{x} + 5 \cdot (-3) $$ 4. **Simplify each term:** - $\sqrt{x} \cdot \sqrt{x} = x$ - $\sqrt{x} \cdot (-3) = -3\sqrt{x}$ - $5 \cdot \sqrt{x} = 5\sqrt{x}$ - $5 \cdot (-3) = -15$ So, $$ x - 3\sqrt{x} + 5\sqrt{x} - 15 $$ 5. **Combine like terms:** $$ -3\sqrt{x} + 5\sqrt{x} = 2\sqrt{x} $$ 6. **Final simplified expression:** $$ x + 2\sqrt{x} - 15 $$ **Answer:** $x + 2\sqrt{x} - 15$