Find the third angle in triangle PQR.

The sum of angles in a triangle is $180^\circ$.

$$\angle PQR = 180^\circ - \angle RPQ - \angle QRP$$ $$\angle PQR = 180^\circ - 60^\circ - 50^\circ$$ $$\angle PQR = 70^\circ$$

The Sine Rule states that for a triangle with sides p, q, r and opposite angles P, Q, R:

$$\frac{p}{\sin P} = \frac{q}{\sin Q} = \frac{r}{\sin R}$$

In triangle PQR, we want to find side PQ (let's call it $r$), and we know angle QRP (R). We also know side RP (let's call it $q$) and angle PQR (Q).

$$\frac{PQ}{\sin(\angle QRP)} = \frac{RP}{\sin(\angle PQR)}$$

Substitute the given values:

$$\frac{PQ}{\sin(50^\circ)} = \frac{6.5}{\sin(70^\circ)}$$

Solve for PQ:

$$PQ = \frac{6.5 \times \sin(50^\circ)}{\sin(70^\circ)}$$ $$PQ = \frac{6.5 \times 0.7660}{0.9397}$$ $$PQ = \frac{4.979}{0.9397}$$ $$PQ \approx 5.30 \text{ units}$$

The length of PQ is approximately 5.30.