To solve the expression $\frac{100}{4}(2+3)$, follow the order of operations (PEMDAS/BODMAS):

1. Parentheses: First, solve the expression inside the parentheses. $2 + 3 = 5$

2. Division: Then, divide $100$ by $4$. $\frac{100}{4} = 25$

3. Multiplication: Finally, multiply the result by $5$ (from the parentheses). $25 \times 5 = 125$

So, the answer is $\boxed{125}$.

Would you like a more detailed explanation or have any questions? Here are five related questions you might find interesting:

1. What is the order of operations and why is it important in solving expressions?
2. How would the expression change if parentheses were added around the entire division?
3. What happens if you change the division to multiplication in the original problem?
4. Can you solve the expression if it were written as $\frac{100}{4} \times (2+3)$?
5. How would the answer change if the original numbers were fractions instead of integers?

Tip: Always remember to follow the order of operations strictly to avoid common mistakes in solving mathematical expressions!