To solve this equation, we first need to simplify it by combining like terms:

5^(x+1) + 5^x + 5^(x-1) = 31

Next, we can rewrite the terms in terms of the same base (5):

5 5^x + 5^x + (1/5) 5^x = 31

Simplify further:

5^x(5 + 1 + 1/5) = 31

5^x(25/5 + 5/5 + 1/5) = 31

5^x(31/5) = 31

Now we can solve for x:

5^x = 31 / (31/5)

5^x = 5

x = 1

Therefore, the solution to the equation is x = 1.