\(\frac{5a+7b}{6a+5b}=\frac{29}{28}\)
\(\Leftrightarrow28\left(5a+7b\right)=29\left(6a+5b\right)\)
\(\Leftrightarrow140a+196b=174a+145b\)
\(\Leftrightarrow34a=51b\)
\(\Leftrightarrow\frac{a}{b}=\frac{51}{34}\)
\(\Leftrightarrow\hept{\begin{cases}a=51\\b=34\end{cases}}\)