По определению косинуса из треугольника ABC:
\(\cos A = \frac{{AC}}{{AB}}\,\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\,\frac{7}{{25}} = \frac{{AC}}{5}\,\,\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\,\,AC = \frac{7}{5}\).
Воспользуемся теоремой Пифагора:
\(B{C^2} + A{C^2} = A{B^2}\,\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\,\,\,BC = \sqrt {{5^2} — {{\left( {\frac{7}{5}} \right)}^2}} = \sqrt {\frac{{576}}{{25}}} = \frac{{24}}{5} = 4,8\).
Ответ: 4,8.