To solve this equation, we can rewrite it using the properties of exponents:

5^x + 5^(x+1) + 5^(x+2) = 31

Since all the terms have a common base of 5, we can combine them using the exponent rule for addition:

5^x + 5^x * 5^1 + 5^x * 5^2 = 31

Now, we can simplify further:

5^x + 5^x * 5 + 5^x * 25 = 31

Next, we can factor out 5^x:

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

Simplifying the expression inside the parentheses:

5^x(31) = 31

Now, we can divide both sides of the equation by 31:

5^x = 1

Since any number raised to the power of 0 is equal to 1, we can conclude that x = 0.