1. Convert mixed numbers to improper fractions: $$25\frac{5}{8} = \frac{205}{8}$$, $$18\frac{3}{4} = \frac{75}{4}$$.
2. Find a common denominator (8): $$\frac{75}{4} = \frac{150}{8}$$.
3. Add the fractions: $$\frac{205}{8} + \frac{150}{8} = \frac{355}{8} = 44\frac{3}{8}$$.