1. **State the problem:** We have two similar triangles \(\triangle ABC\) and \(\triangle XYZ\). Given sides are \(AB=5\), \(AC=7\), and unknown side \(BC=?\) in \(\triangle ABC\), and sides \(XY=45\), \(YZ=72\), and \(XZ=63\) in \(\triangle XYZ\). We need to find the length of side \(BC\). 2. **Recall the property of similar triangles:** Corresponding sides of similar triangles are proportional. This means \(\frac{AB}{XY} = \frac{AC}{XZ} = \frac{BC}{YZ}\). 3. **Identify corresponding sides:** Since \(AB\) corresponds to \(XY\), \(AC\) corresponds to \(XZ\), and \(BC\) corresponds to \(YZ\). 4. **Calculate the scale factor:** Using \(AB\) and \(XY\), the scale factor is \(k = \frac{AB}{XY} = \frac{5}{45} = \frac{1}{9}\). 5. **Verify scale factor with another pair:** Using \(AC\) and \(XZ\), \(\frac{AC}{XZ} = \frac{7}{63} = \frac{1}{9}\), confirming the scale factor is consistent. 6. **Find the missing side \(BC\):** Using the proportion \(\frac{BC}{YZ} = \frac{1}{9}\), so \(BC = \frac{YZ}{9} = \frac{72}{9} = 8\). **Final answer:** \(\boxed{8}\) is the length of side \(BC\) in \(\triangle ABC\).