The five-digit number $345xy$ is divisible by 80. The value of $x+y$ is:

80 = $8\times 10$, so the number must end in 0, giving $y=0$. Then $345\times 0=10\times (3450+x)$, and this is a multiple of 80 only when $3450+x$ is a multiple of 8. Since $3450=8\times 431+2$, we need $x=6$. The number is $34560=80\times 432$, so $x+y=6+0=6$.