1. **State the problem:** Simplify the expression $5\sqrt{13} - 2\sqrt{13}$. 2. **Identify like terms:** Both terms contain $\sqrt{13}$, so they are like terms and can be combined by subtracting their coefficients. 3. **Apply the subtraction:** $$5\sqrt{13} - 2\sqrt{13} = (5 - 2)\sqrt{13}$$ 4. **Simplify the coefficients:** $$= 3\sqrt{13}$$ 5. **Final answer:** The simplified form of the expression is $3\sqrt{13}$.