Using the properties of logarithms, we can simplify the expression:

$\log 25 + \log 5 + \log 80$

The logarithm addition rule states:

$\log a + \log b = \log (a \cdot b)$

Applying this to the expression:

$\log 25 + \log 5 + \log 80 = \log (25 \cdot 5 \cdot 80)$

Now calculate the product:

$25 \cdot 5 = 125$ $125 \cdot 80 = 10,000$

Thus, the expression simplifies to:

$\log 10,000$

Since $\log 10,000 = 4$ (because $10,000 = 10^4$), the final answer is:

$\boxed{4}$

Would you like further explanation or have any questions? Here are five related questions to explore:

1. How can the logarithm properties simplify other expressions?
2. What is the logarithmic relationship between multiplication and addition?
3. How would you handle expressions with negative logarithms?
4. What happens if logarithmic bases are different in the equation?
5. Can logarithmic identities help in solving real-world problems?

Tip: Remember, $\log a + \log b = \log (a \cdot b)$ only applies when both logarithms have the same base!