imc

It is a well-known fact that the sum of the first $n$ odd numbers is $n^2$. This makes the sum of the first $8$ odd numbers equal to $64$. Let $n$ be equal to the smallest of the $5$ even integers. Then $(n+2)$ is the next highest, $(n+4)$ even higher, and so on. This sets up the equation $n+(n+2)+(n+4)+(n+6)+(n+8)+4=64$ Now we solve: $$5n+24=64$$ $$5n=40$$ $$n=8$$ Thus, the smallest integer is $\boxed{8}$.