Triangle Extension Calculations

In triangle ABC, the lengths of the sides are given by AB= 7, BC= 10, and CA= 5. A line segment DE is drawn parallel to side AC, thus creating triangles ABD and CDE, which are similar to each other. If the length of DE is 3, what is the length of segment AB when extended to meet line DE?

Use the property of similar triangles, which states that the ratios of corresponding sides are equal.