4. If the prime numbers $m, n$ satisfy $5 m+7 n=129$, then the value of $m+n$ is $\qquad$ .
\&. The original wing converts to $5 m \equiv 129(\bmod 7)$, i.e., $5 m \equiv 3$ (modi), solving yields $m \equiv 2(\bmod 7)$. Given that $m$ is a prime number, and from the original indeterminate equation, $m<25$. Therefore, the possible values of $\boldsymbol{m}$ are 2 or 23. Checking, when $m=2$, $n=17$, thus, $m+n=19$; when $m=23$, $n=2, m+n=25$, i.e., the value of $m+n$ is 19 or 25.