The expression "five more than half of $x$" can be broken down as follows:

1. "Half of $x$" is written as $\frac{x}{2}$.
2. "Five more than" means you add 5 to that value.

Thus, the expression is:

$\frac{x}{2} + 5$

Would you like a detailed explanation or examples of similar expressions? Here are some related questions for you to explore:

1. How would you write "three less than twice a number" in algebraic form?
2. What is the algebraic representation of "half of a number is 7"?
3. How do you express "ten more than a number $y$"?
4. What is the difference between "three times a number" and "three more than a number" in terms of expressions?
5. Can you solve for $x$ in the equation $\frac{x}{2} + 5 = 12$?

Tip: Always be mindful of the order of operations when writing and interpreting expressions, especially with phrases like "more than" or "less than." These often imply addition or subtraction after applying other operations.