Answer
False
Work Step by Step
The left side can be written:
$\log_b(xy)^5=5\log_b(xy)=5(\log_b x+\log_b y)$
Thus,
$\log_{b}(xy)^5\ne(\log_{b}x+\log_{b}y)^5.$.
Therefore, the statement is false.
A correct statement is:
$\log_b(xy)^5=5\log_b(xy)=5(\log_b x+\log_b y)$
