[tex]\tanh(x)=\frac{\sinh(x)}{\cosh(x)}\rightarrow \sinh(x)=\cosh(x)\tanh(x)[/tex]
Now,
[tex]\cosh^2(x)-\sinh^2(x)=1[/tex]
so substituting for sinh(x):
[tex]\cosh^2(x)-\cosh^2(x)\tanh^2(x)=1\rightarrow \cosh^2(x)(1-\tanh^2(x))=1[/tex]
which means
[tex]\cosh(x)=\pm\sqrt{\frac{1}{1-\tanh^2(x)}}=\pm\sqrt{\frac{1}{1-(\frac{5}{13})^2}}=\pm\sqrt{\frac{1}{1-\frac{25}{169}}}=\pm\sqrt{\frac{1}{\frac{144}{169}}}= \pm\frac{13}{12}
\\
\\[/tex]
