To solve this exponential equation, we can first rewrite it using the properties of exponents.

(2^5)^(5-x) = (4/25)^2

Rewrite the left side using the property (a^b)^c = a^(b*c):

2^(5*(5-x)) = (4/25)^2

2^(25-5x) = (4/25)^2

Next, simplify both sides by calculating the exponents:

2^(25-5x) = (16/625)

Next, rewrite the fraction on the right side as a power of 2:

2^(25-5x) = 2^4 / 2^8

Apply the property a^(m)/a^(n) = a^(m-n):

2^(25-5x) = 2^(-4)

Now that the bases are the same, we can set the exponents equal to find the value of x:

25-5x = -4

-5x = -29

x = 29/5

Therefore, the solution to the equation is x = 29/5 or 5.8.