$\huge \begin{align} f'(x) &= 6^x \\ f(4) &= -5 \\ f(x)&= \int_{0}^{x} e^{x\ln 6}\d x \\ &= e^{x\ln 6} \frac{1}{\ln 6} + C\\ \\ f(4) = -5 &= \frac{e^{4\ln 6}}{\ln 6} + C \\ \\ C &=-5 -\frac{e^{4\ln 6}}{\ln 6} \\ f(x) &= \frac{e^{x\ln{6}}}{\ln 6} - 5 - \frac{e^{4\ln 6}}{\ln 6} \end{align}$