1. **State the problem:** Simplify the expression $$\frac{25}{4} + 5$$. 2. **Recall the rule:** To add a fraction and a whole number, convert the whole number to a fraction with the same denominator. 3. Convert 5 to a fraction with denominator 4: $$5 = \frac{5 \times 4}{4} = \frac{20}{4}$$. 4. Add the fractions: $$\frac{25}{4} + \frac{20}{4} = \frac{25 + 20}{4} = \frac{45}{4}$$. 5. The simplified result is $$\frac{45}{4}$$ or as a mixed number $$11 \frac{1}{4}$$. **Final answer:** $$\frac{45}{4}$$.