1. The problem is to write the expression $\frac{11}{3} + \frac{q}{5}$ as a single fraction in simplest form. 2. To add fractions, they must have a common denominator. The denominators here are 3 and 5. 3. The least common denominator (LCD) of 3 and 5 is 15. 4. Convert each fraction to an equivalent fraction with denominator 15: $$\frac{11}{3} = \frac{11 \times 5}{3 \times 5} = \frac{55}{15}$$ $$\frac{q}{5} = \frac{q \times 3}{5 \times 3} = \frac{3q}{15}$$ 5. Now add the fractions: $$\frac{55}{15} + \frac{3q}{15} = \frac{55 + 3q}{15}$$ 6. The expression as a single fraction in simplest form is: $$\boxed{\frac{55 + 3q}{15}}$$ This is the final answer.