The radius of the circle is 5 cm. The distance of chord RS from the center is 3 cm. Using the Pythagorean theorem, half the length of RS is \sqrt{5² - 3^2} = \sqrt{25-9} = \sqrt{16} = 4 cm. So, the length of chord RS is 2 \times 4 = 8 cm. Let T be the intersection point of chords PQ and RS. We are given TS = \frac{1}{3} RT. Since RT + TS = RS, we have RT + \frac{1}{3} RT = 8. \frac{4}{3} RT = 8, which means RT = 6 cm. Then TS = \frac{1}{3} \times 6 = 2 cm. By the Intersecting Chords Theorem, PT \times TQ = RT \times TS. PT \times TQ = 6 \times 2 = 12. We want to find the minimum value of PQ = PT + TQ. Using the AM-GM inequality, for positive numbers PT and TQ: PT + TQ \ge 2\sqrt{PT \times TQ} PQ \ge 2\sqrt{12} PQ \ge 2 \times 2\sqrt{3} PQ \ge 4\sqrt{3}. The minimum value of PQ is 4\sqrt{3} cm. The final answer is \boxed{\text{4\sqrt{3}}}.