1. Convert mixed numbers to improper fractions: $$25\frac{7}{24} = \frac{607}{24}$$, $$19\frac{31}{36} = \frac{684+31}{36} = \frac{715}{36}$$.
2. Find a common denominator (72): $$\frac{607}{24} = \frac{607 \times 3}{24 \times 3} = \frac{1821}{72}$$, $$\frac{715}{36} = \frac{715 \times 2}{36 \times 2} = \frac{1430}{72}$$.
3. Subtract the fractions: $$\frac{1821}{72} - \frac{1430}{72} = \frac{391}{72} = 5\frac{31}{72}$$.