The inverse z-transform of X(z)=5z(z−1)2−2z(z−0.5)2𝑋(𝑧)=5𝑧(𝑧−1)2−2𝑧(𝑧−0.5)2 will be:

The inverse z-transform of a function X(z) can be found by using the formula for the inverse z-transform, which is given by:

x[n] = (1/2πj) ∫_C X(z)z^(n-1) dz

where C is a counterclockwise closed path encircling the origin and entirely in the region of convergence (ROC) of X(z).

However, the function you've provided seems to be written incorrectly or incompletely. It's written twice and there's no operation (like addition, subtraction, multiplication, or division) between them.

If the function is X(z) = 5z/(z-1)^2 - 2z/(z-0.5)^2, then we can use the method of partial fraction expansion to simplify the function and then use the standard z-transform pairs to find the inverse z-transform.

If the function is X(z) = 5z*(z-1)^2 - 2z*(z-0.5)^2, then it's a bit more complicated and might not have a simple inverse z-transform that can be expressed in a closed form.

In either case, you would need to clarify the function before we can proceed with finding its inverse z-transform.