This question involves a geometric figure with points on a circle. The goal is to determine the length of segment $PQ$.

To proceed, we need to use information about the circle and the relationships between the points, such as the chord and secant theorems. The key elements given are:

• The lengths of the segments $PS = 8.5$ cm, $QS = 5$ cm, and $RS = 3$ cm.
• The line segments $TSR$ and $PQR$ are straight lines.

This setup seems like a problem involving a circle and some properties of cyclic quadrilaterals or secants. However, it's hard to discern specific relationships from the image alone.

To find the length of $PQ$, it would help to know if we can apply a specific rule like the Power of a Point, or perhaps further steps involving angles or chord properties.

Would you like me to guide you step-by-step, or do you have more specific instructions or information about the question?