Answer
$(b)$
Work Step by Step
Let us solve the given problem in the following way:
$m^2-2m-15=0$
or, $m^2-5m+3m-15=0$
or, $(m+3)(m-5)=0$
This can be written as : $m+3=0$ or, $m-5=0$
Thus, $m=-3,5$
Hence, the final answer will be $(b)$.