Problem:
Given that xy = 5 and xy = 6, we need to find the value of x^3y^3.

Solution:

Step 1: Understand the given information
- We are given that xy = 5 and xy = 6.
- This means that x and y are two numbers whose product is 5 and 6 respectively.

Step 2: Solve for x and y
To find the values of x and y individually, we can set up two equations using the given information.

Equation 1: xy = 5
Equation 2: xy = 6

Step 3: Solving the equations
Equation 1: xy = 5
We can rewrite this equation as:
y = 5/x

Substituting this value of y into Equation 2, we get:
x * (5/x) = 6
Simplifying further:
5 = 6

Step 4: Analyzing the contradiction
From the simplification above, we can see that the equation 5 = 6 is not true. This implies that there is no solution for x and y that satisfies both equations xy = 5 and xy = 6 simultaneously.

Step 5: Conclusion
Since there is no solution for x and y that satisfies both equations, it is not possible to determine the value of x^3y^3.