Domain vs Codomain

Consider the function $f(x)=x+5$ on domain $X=\{x \mid 5 \leq x \leq 29\}.$ The codomain of $f(x)$ is $Y=\{y \mid a \leq y \leq b\}$ . If the constants $a$ and $b$ are such that the inverse function of $f(x)$ exists, then what is the value of $a+b$ ?