jmc

We start with $125=5^3$ cans. After recycling these cans, we will have made $125\cdot \frac{1}{5}=5^2$ new cans. We can then recycle these new cans to make $5^2\cdot \frac{1}{5}=5$ new cans and then finally recycle these to make $5\cdot \frac{1}{5}=1$ new can. So the total number of new cans is $5^2+5+1=25+5+1=\boxed{31}$.