jmc

First we begin by solving the system of equations $$\begin{array}{rl}5a+2b& =0,\\ b-2& =a.\end{array}$$Making the substitution for $a$ from the second equation to the first, we get $5(b-2)+2b=0$, which simplifies to $7b-10=0$. Solving for $b$, we find that $b=\frac{10}{7}$. Hence $7b=7\cdot \frac{10}{7}=\boxed{10}$.