1. **State the problem:** We need to find the perimeter of quadrilateral ADBC given that $AC=5$ cm, $BC=3$ cm, and $CB=DB$. 2. **Analyze the given information:** Since $CB=DB$, the points B, C, and D form an isosceles triangle with $BC=DB=3$ cm. 3. **Identify the sides of quadrilateral ADBC:** The quadrilateral consists of sides $AD$, $DB$, $BC$, and $CA$. 4. **Find the length of $AD$:** Since triangles $ABC$ and $ABD$ are congruent (from part 1), corresponding sides are equal. Therefore, $AD = AC = 5$ cm. 5. **Calculate the perimeter:** $$\text{Perimeter} = AD + DB + BC + CA = 5 + 3 + 3 + 5 = 16 \text{ cm}$$ **Final answer:** The perimeter of quadrilateral ADBC is $16$ cm.