To solve this equation, we can first factor the denominator of the last term on the right side:

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

Now we can rewrite the equation:

5/(x - 1) - 3/(x + 1) = 15/((x - 1)(x + 1))

Multiplying all terms by (x - 1)(x + 1) to clear the denominators, we get:

5(x + 1) - 3(x - 1) = 15

Expanding the terms:

5x + 5 - 3x + 3 = 15

Combine like terms:

2x + 8 = 15

Subtract 8 from both sides:

2x = 7

Divide by 2:

x = 7/2

Therefore, the solution to the equation is x = 7/2.