To solve this equation, we can simplify the left side of the equation first.

Using the rule of exponents, we know that (a^m)^n = a^(m*n). Therefore, we can rewrite (1/5)^3 as 1/5^(3).

Now, we can rewrite the equation as:

5^n * 1/5^3 = 125

Next, we can simplify the equation further by using the rule of exponents again. We know that a^(-n) = 1/a^n. Therefore, we can rewrite 1/5^3 as 5^(-3).

Now, the equation becomes:

5^n * 5^(-3) = 125

Using the rule of exponents again, we know that a^m * a^n = a^(m+n). Therefore, we can simplify the equation further by adding the exponents:

5^(n + (-3)) = 125

Simplifying the exponent on the left side of the equation:

5^(n - 3) = 125

Now, we can rewrite 125 as 5^3:

5^(n - 3) = 5^3

Since the bases are the same, we can equate the exponents:

n - 3 = 3

Solving for n:

n = 3 + 3

n = 6

Therefore, the value of n that satisfies the equation is 6.