Convert mixed numbers to improper fractions: $$3 \frac{3}{4} = \frac{15}{4}$$ and $$5 \frac{5}{6} = \frac{35}{6}$$. Find a common denominator (12): $$\frac{15}{4} = \frac{45}{12}$$ and $$\frac{35}{6} = \frac{70}{12}$$. Subtract: $$\frac{45}{12} - \frac{70}{12} = -\frac{25}{12}$$.
Answer: -25/12