To solve this equation, we need to use the properties of logarithms.

We start by combining the logs on the left side using the properties of logarithms:

log5(x^2 - 1) - log5(x - 1) = 1

Next, we can use the property that states log(a) - log(b) = log(a/b):

log5((x^2 - 1)/(x - 1)) = 1

Now, we can rewrite the equation in exponential form:

5^1 = (x^2 - 1)/(x - 1)

5 = (x^2 - 1)/(x - 1)

Now, we can cross multiply to solve for x:

5(x - 1) = x^2 - 1

5x - 5 = x^2 - 1

Rearranging the equation, we get:

x^2 - 5x - 4 = 0

Now, we can factor the quadratic equation:

(x - 4)(x + 1) = 0

Setting each factor to zero, we get:

x - 4 = 0 or x + 1 = 0

Therefore, the solutions to the equation are x = 4 and x = -1.