Chapter 7: Transcendental Functions - Section 7.7 - Hyperbolic Functions - Exercises 7.7 - Page 431: 61

$\displaystyle \ln(\frac{2}{3})$

Substitute into the relevant formula: $\displaystyle \sinh^{-1}(-\frac{5}{12})=\ln(-\frac{5}{12}+\sqrt{\frac{25}{144}+1})$ $=\displaystyle \ln(-\frac{5}{12}+\sqrt{\frac{169}{144}})$ $=\displaystyle \ln(-\frac{5}{12}+\frac{13}{12})$ $=\displaystyle \ln(\frac{8}{12})$ =$\displaystyle \ln(\frac{2}{3})$