如图, 在 $\triangle A B C$ 中, $\overrightarrow{B D}=4 \overrightarrow{D C}$, 则 $\overrightarrow{A D}=(\quad)$
A. $\frac{1}{5} \overrightarrow{A B}+\frac{4}{5} \overrightarrow{A C}$
B. $\frac{4}{5} \overrightarrow{A B}+\frac{1}{5} \overrightarrow{A C}$
C. $\frac{1}{6} \overrightarrow{A B}+\frac{5}{6} \overrightarrow{A C}$
D. $\frac{5}{6} \overrightarrow{A B}+\frac{1}{6} \overrightarrow{A C}$