jmc

When we rewrite the base numbers in terms of $b$, we get the equation $$5\cdot (2b+3)=b^2+5b+1\Rightarrow b^2-5b-14=0.$$ Solving this quadratic equation, we get $b=7$ and $b=-2$. But, since the base must be positive, $b=\boxed{7}$.