To solve this inequality, we first need to convert the expression involving the cube root of 5 to a fractional exponent:

1/3√5 = 5^(1/3)

Now, the inequality becomes:

25^(-2x/5) > 5^(1/3)

Next, we can rewrite 25 and 5 in terms of the same base (5):

5^2 = 25

Now, the inequality becomes:

(5^2)^(-2x/5) > 5^(1/3)

Using the properties of exponents, we can simplify further:

5^(-4x/5) > 5^(1/3)

Now, we can equate the exponents:

-4x/5 > 1/3

Multiplying both sides by 5 to get rid of the fraction:

-4x > 5/3

Dividing by -4 to isolate x:

x < -5/12

Therefore, the solution to the inequality is x < -5/12.