To solve the equation (1/3)^(2x-1) = 3^5, we can start by simplifying both sides of the equation.

First, let's simplify the right side of the equation: 3^5 = 3 * 3 * 3 * 3 * 3 = 243.

Now, let's simplify the left side of the equation: (1/3)^(2x-1) = (1/3)^(2x) * (1/3)^(-1) = (1/3)^(2x) * 3.

So now our equation becomes (1/3)^(2x) * 3 = 243.

Next, let's isolate the term with the variable by dividing both sides of the equation by 3: (1/3)^(2x) = 243/3 = 81.

To simplify further, we can rewrite 81 as (3^4): (1/3)^(2x) = (3^4).

Now, we can rewrite the left side of the equation using exponential notation: 3^(-2x) = 3^4.

Since the bases are the same, we can set the exponents equal to each other: -2x = 4.

To solve for x, divide both sides of the equation by -2: x = 4/(-2) = -2.

Therefore, the solution to the equation (1/3)^(2x-1) = 3^5 is x = -2.