\(a:b=3:5\to\dfrac{a}{b}=\dfrac{3}{5}\\\\a:c=5:7\to\dfrac{a}{c}=\dfrac{5}{7}\\\\\dfrac{a}{c}:\dfrac{a}{b}=\dfrac{a}{c}\cdot\dfrac{b}{a}=\dfrac{b}{c}\\\\therefore\ \dfrac{b}{c}=\dfrac{5}{7}:\dfrac{3}{5}=\dfrac{5}{7}\cdot\dfrac{5}{3}=\dfrac{25}{21}\\\\Answer:\boxed{\frac{b}{c}=\frac{25}{21}\to a:c=25:21}\)
