To solve the equation (5^{x+1} - 2*5^{x-1} - 23 = 0), we can first simplify the equation:

(5^{x+1} = 5^x 5 = 55^x)

(25^{x-1} = 25^x/5 = 2/5 * 5^x)

So the equation becomes:

(55^x - 2/55^x - 23 = 0)

Simplify further:

(5^x (5 - 2/5) - 23 = 0)

(5^x (25/5 - 2/5) - 23 = 0)

(5^x (23/5) - 23 = 0)

(23/5 * 5^x = 23)

(5^x = 5)

Now we have a simple exponential equation where the base is the same on both sides. Therefore, (x = 1).