jmc

If the first time was in May, the second time will be 5 months after May, the third time will be $5\cdot 2$ months after May, etc. That means the 25th time will be $5\cdot 24$ months away. Since the months repeat every 12 months, we look for the remainder when $5\cdot 24$ is divided by 12 and add that many months to May. We notice that $\frac{5\cdot 24}{12}=5\cdot 2$, so it turns out that $5\cdot 24$ is a multiple of 12 and leaves a remainder of 0 when divided by 12. So the 25th time will be a certain number of years afterward but still in the same month, $\boxed{\text{May}}$.