1. **State the problem:** Simplify the expression $$3q + 10 + \frac{5}{3q^5 r^5}$$ and express it as a single fraction in simplest form. 2. **Rewrite the expression:** To combine all terms into a single fraction, write the whole expression with a common denominator $$3q^5 r^5$$: $$3q + 10 + \frac{5}{3q^5 r^5} = \frac{3q \cdot 3q^5 r^5}{3q^5 r^5} + \frac{10 \cdot 3q^5 r^5}{3q^5 r^5} + \frac{5}{3q^5 r^5}$$ 3. **Multiply the numerators:** $$3q \cdot 3q^5 r^5 = 9q^{6} r^{5}$$ $$10 \cdot 3q^5 r^5 = 30q^{5} r^{5}$$ 4. **Combine all terms over the common denominator:** $$\frac{9q^{6} r^{5} + 30q^{5} r^{5} + 5}{3q^{5} r^{5}}$$ 5. **Factor the numerator:** Factor out the greatest common factor, which is 1 (no common factor for all terms), but notice the first two terms share $$3q^{5} r^{5}$$: $$9q^{6} r^{5} + 30q^{5} r^{5} = 3q^{5} r^{5} (3q + 10)$$ So numerator becomes: $$3q^{5} r^{5} (3q + 10) + 5$$ 6. **Final expression:** $$\frac{3q^{5} r^{5} (3q + 10) + 5}{3q^{5} r^{5}}$$ This is the simplest single fraction form. **Answer:** $$\boxed{\frac{3q^{5} r^{5} (3q + 10) + 5}{3q^{5} r^{5}}}$$