To solve this equation, we can start by simplifying both sides of the equation.

On the left side, we have (1/3)^(2x-1). To simplify this, we can use the property of exponents that states (a^b)^c = a^(b*c). Applying this property, we get:

(1/3)^(2x-1) = (1/3)^(2*(x-1))

Next, we can simplify the right side of the equation, which is (1/3)^5.

Now, we have:

(1/3)^(2x-1) = (1/3)^(2*(x-1)) = (1/3)^5

Since the bases are the same on both sides of the equation, we can set the exponents equal to each other:

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

Now, we can solve for x:

2x-1 = 5

Adding 1 to both sides:

2x = 6

Dividing both sides by 2:

x = 3

Therefore, the solution to the equation is x = 3.