To solve this inequality, we can first convert both sides to exponential form:

1/3^(log1/3(2x + 5)) > 1/3^(log1/3(x - 1))

This simplifies to:

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

Now, we raise both sides to the power of 3 to eliminate the cube root:

(2x + 5) > (x - 1)

Now, we can solve for x:

2x + 5 > x - 1
x > -6

Therefore, the solution to the inequality is x > -6.