1. **State the problem:** Simplify the expression $\sqrt{3} + \sqrt{5}$. 2. **Understand the terms:** $\sqrt{3}$ and $\sqrt{5}$ are square roots of 3 and 5 respectively. They are irrational numbers and cannot be simplified further. 3. **Check if terms can be combined:** Since $\sqrt{3}$ and $\sqrt{5}$ are unlike terms (different radicands), they cannot be added together into a single square root or simplified further. 4. **Final answer:** The expression remains $\sqrt{3} + \sqrt{5}$ as it is already in simplest form.