$\begin{aligned} & \text {} \sinh x=\frac{5}{12} \\ & \because \cosh x=2 \cosh \frac{x}{2}-1=\sqrt{1+\sin h^2 \frac{x}{2}} \\ & \Rightarrow 2 \cosh ^2 \frac{x}{2}-1=\sqrt{1+\left(\frac{5}{12}\right)^2} \\ & \Rightarrow 2 \cosh ^2 \frac{x}{2}=\frac{13}{12}+1=\frac{25}{12} \Rightarrow \cosh \frac{x}{2}=\sqrt{\frac{25}{24}}=\frac{5}{2 \sqrt{6}}\end{aligned}$