jmc

There are five digits greater than $4$ (5, 6, 7, 8, and 9), and each of the first three zip code digits could be any of them. Hence, there are $5\cdot 5\cdot 5=125$ ways to choose the first three digits. The last two zip code digits have no restrictions, so there are $10\cdot 10=100$ ways to choose them. Thus, there are $125\cdot 100=\boxed{12500}$ such zip codes.