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

5^(2x-1) = 0.4 2^(2x-1)
5^(2x-1) = 4/10 2^(2x-1)
5^(2x-1) = 2/5 * 2^(2x-1)
5^(2x-1) = 2^(2x-1) / 5^(1)

Now, we can rewrite the equation to have the same base:

(5/10)^(2x-1) = 2^(2x-1) / 5

Now, we can rewrite 5/10 as 1/2:

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

Now, we can rewrite 1/2 as 2^-1:

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

Now that the bases are the same, we can equate the exponents:

-2x + 1 = 2x - 1

Now, let's solve for x:

-2x + 1 = 2x - 1
1 = 4x - 1
2 = 4x
x = 2/4
x = 1/2

Therefore, the solution to the equation 5^(2x-1) = 0.4 * 2^(2x-1) is x = 1/2.