Answer
$$\sinh \ln 5= \frac{12}{5}, \quad \tanh (3\ln 5) =\frac{7812}{7813}.$$
Work Step by Step
Using the fact that $x=e^{\ln x}$, we have
$$\sinh \ln 5=\frac{e^{\ln 5}-e^{-\ln 5}}{2}=\frac{5-(1/5)}{2}=\frac{12}{5}$$
$$\tanh (3\ln 5)=\frac{e^{3\ln 5}-e^{-3\ln 5}}{e^{3\ln 5}+e^{-3\ln 5}}=\frac{5^3-5^{-3}}{5^3+5^{-3}}=\frac{7812}{7813}.$$
