To solve the equation, we can rewrite it as:

5^n + 5^(n-2) = 130

Now, let's simplify the equation by combining the terms with the same base:

5^n + (1/25) * 5^n = 130

To combine the terms, we need to have the same denominator. So, let's multiply the second term by 25:

5^n + (25/25) * 5^(n-2) = 130

5^n + 25 * 5^(n-2) = 130

Now, let's simplify the equation further:

5^n + 25 * (5^n / 5^2) = 130

5^n + 25 * (5^n / 25) = 130

5^n + 5^n = 130

2 * 5^n = 130

Divide both sides of the equation by 2:

5^n = 65

Now, we need to find the value of n that satisfies this equation. Taking the logarithm of both sides of the equation can help us find the value of n:

log(5^n) = log(65)

n * log(5) = log(65)

Divide both sides of the equation by log(5):

n = log(65) / log(5)

Using a calculator, we can find that:

n ≈ 2.191

Therefore, the value of n that satisfies the equation is approximately 2.191.