Answer
$$r = - \frac{1}{5}$$
Work Step by Step
$$\eqalign{
& {\text{Let the sequence }} - 25,\,\,5,\,\, - 1,\,\,\frac{1}{5},\,\,... \cr
& {a_1} = - 25,\,\,\,{a_2} = 5 \cr
& {\text{The common ratio is }} \cr
& r = \frac{{{a_2}}}{{{a_1}}} = \frac{5}{{ - 25}} \cr
& {\text{Simplifying}} \cr
& r = - \frac{1}{5} \cr} $$