To solve this problem, we can use the properties of tangents and chords in a circle. Let's break down the solution into steps:

Step 1: Draw the diagram
Draw a circle with center O and radius 5 cm. Draw diameter PQ and the tangent XPY at one end of the diameter. Also, draw chord AB parallel to XY and at a distance of 8 cm from P.

Step 2: Identify the given information
We are given that the radius of the circle is 5 cm and the distance of chord AB from P is 8 cm.

Step 3: Use the properties of tangents and chords
Since XPY is a tangent to the circle, we know that the angle XPY is 90 degrees. Therefore, triangle XPY is a right triangle.

Step 4: Find the length of XY
Using the Pythagorean theorem, we can find the length of XY. Let's denote XY as x.
By the Pythagorean theorem, we have:
XP^2 + PY^2 = XY^2
Since XP is a radius of the circle, it is equal to 5 cm.
Similarly, PY is also a radius of the circle, so it is also equal to 5 cm.
Substituting these values into the equation, we get:
5^2 + 5^2 = x^2
25 + 25 = x^2
50 = x^2
Taking the square root of both sides, we get:
x = √50
Simplifying, we get:
x ≈ 7.07 cm

Step 5: Use the properties of parallel chords
Since AB is parallel to XY, we know that the distance between AB and XY is constant. In this case, the distance is given as 8 cm.

Step 6: Find the length of AB
Let's denote the length of AB as y.
Since AB is parallel to XY, we can create a right triangle APB by drawing a perpendicular line from B to XP.
In triangle APB, AB is the hypotenuse, and the length of the perpendicular line from B to XP is 8 cm.
Using the Pythagorean theorem, we have:
AP^2 + PB^2 = AB^2
Since AP is a radius of the circle, it is equal to 5 cm.
Substituting the values into the equation, we get:
5^2 + 8^2 = y^2
25 + 64 = y^2
89 = y^2
Taking the square root of both sides, we get:
y ≈ √89
Simplifying, we get:
y ≈ 9.43 cm

Step 7: Determine the correct answer
We need to find the length of chord AB parallel to XY and at a distance of 8 cm from P. From our calculations, we found that the length of AB is approximately 9.43 cm. None of the given options match this value, so the correct answer is none of the given options.

In conclusion, the correct answer to this problem is none of the given options.