По основному тригонометрическому тождеству:
\({\sin ^2}A + {\cos ^2}A = 1\,\,\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\,\,\cos A = \sqrt {1 — \frac{{49}}{{625}}} = \sqrt {\frac{{576}}{{625}}} = \frac{{24}}{{25}}\).
По определению косинуса из треугольника ABC:
\(\cos A = \frac{{AC}}{{AB}}\,\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\,\frac{{24}}{{25}} = \frac{{4,8}}{{AB}}\,\,\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\,\,AB = \frac{{25 \cdot 4,8}}{{24}} = 5\).
Ответ: 5.