在四边形ABCD中，AB\parallel CD，AD\parallel BC，且\angle BAD，\angle ADC的平分线AE，DF分别交BC于点E，F。若EF=2，AB=5，则AD的长为____。---**Chart/Diagram Description:** * **Type:** Geometric figure. * **Main Elements:** * **Shape:** A parallelogram ABCD. Points are labeled A, B, C, D in a counter-clockwise manner, starting from the top left. * **Lines/Segments:** * Sides of the parallelogram: AB, BC, CD, DA. AB appears parallel to CD, and AD appears parallel to BC. * Points E and F are located on the side BC. F is to the left of E. Both E and F are between B and C. * Line segment AE connects vertex A to point E on BC. * Line segment DF connects vertex D to point F on BC. * Point G is the intersection of line segments AE and DF. * Line segment BD is the diagonal of the parallelogram. * **Labels:** Vertices are labeled A, B, C, D. Points on BC are labeled F, E. The intersection point is labeled G. * **Relative Position and Direction:** ABCD is a parallelogram. E and F are on BC. F is to the left of E. G is the intersection of AE and DF. **Textual Information:** * There is no question stem, options, or other problem text present in the image. Only the geometric figure with labeled points is provided.