To solve the expression $\frac{100}{4}(5)$, follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction).

1. First, divide $100$ by $4$: $\frac{100}{4} = 25$

2. Next, multiply the result by $5$: $25 \times 5 = 125$

Thus, the final answer is $125$.

Would you like more details on the steps or any questions about the process? Here are some related questions to explore further:

1. How does the order of operations work in complex expressions?
2. What happens when parentheses are involved in more complicated expressions?
3. Can you explain how division and multiplication are related?
4. How would you solve $100/(4 \times 5)$?
5. What is the distributive property, and how does it apply to similar problems?

Tip: Always follow the order of operations carefully, especially when both multiplication and division appear in the same expression!