Let's break down the expression step by step:

Given: $5^2 \times \left(\frac{1}{125}\right)^{-1} \div 25$

Step 1: Simplify $5^2$

$5^2 = 25$

Step 2: Simplify $\left(\frac{1}{125}\right)^{-1}$

Taking the reciprocal of $\frac{1}{125}$ gives: $\left(\frac{1}{125}\right)^{-1} = 125$

Step 3: Multiply the results from Step 1 and Step 2

$25 \times 125 = 3125$

Step 4: Divide by 25

$\frac{3125}{25} = 125$

Thus, the value of the expression is: $\boxed{125}$

Do you want more details, or have any questions?

Here are 5 related questions:

1. How do you calculate powers of numbers?
2. What are the rules for dealing with negative exponents?
3. How do you simplify expressions with both multiplication and division?
4. What is the relationship between exponents and roots?
5. How can you apply exponent rules to more complex expressions?

Tip: Remember that any number raised to a negative exponent flips the fraction (reciprocal).