jmc

When we rewrite the base numbers as sums of digit bundles, we get the equation $$5\cdot (2b+5)=b^2+3b+7\Rightarrow b^2-7b-18=0.$$Solving this quadratic equation, we get $b=9$ and $b=-2$. But, since the base must be positive, $b=\boxed{9}$. We can check our answer by verifying that $5\cdot 25_9=137_9$, which turns out to be true.