5. Let $\frac{1+\sin x}{\cos x}=\frac{22}{7}$ and $\frac{1+\cos x}{\sin x}=\frac{m}{n}$, where $\frac{m}{n}$ is in its simplest form, then $m+n=$

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Let $\left\{\begin{array}{l}\sin x=22 k-1, \\ \cos x=7 k\end{array} \Rightarrow k=\frac{44}{533} \Rightarrow\left\{\begin{array}{l}\sin x=\frac{435}{533}, \\ \cos x=\frac{308}{533}\end{array} \Rightarrow \frac{1+\cos x}{\sin x}=\frac{841}{435}=\frac{29}{15}\right.\right.$.
Therefore, $m+n=44$.