1. **State the problem:** Simplify the expression $11x + 7 + 5 : 6 - 7x + 20x$. 2. **Clarify the expression:** The colon $:$ is often used to denote division. So the expression is $11x + 7 + \frac{5}{6} - 7x + 20x$. 3. **Combine like terms:** Group the $x$ terms and constants separately. $$11x - 7x + 20x + 7 + \frac{5}{6}$$ 4. **Simplify the $x$ terms:** $$11x - 7x + 20x = (11 - 7 + 20)x = 24x$$ 5. **Simplify the constants:** $$7 + \frac{5}{6} = \frac{42}{6} + \frac{5}{6} = \frac{47}{6}$$ 6. **Final simplified expression:** $$24x + \frac{47}{6}$$ This is the simplified form of the given expression.