Precalculus, Chapter 9, 9.3, Section 9.3, Problem 26

You need to write the 5 terms of the geometric sequence, hence, since the problem provides the first term, you need the ratio q. You may evaluate the ratio using the relation:
a_(k+1) = a_k*q
q = (a_(k+1))/(a_k) => q = -2
You may evaluate a_2, a_3, a_4, a_5 , such that:
a_2 = a_1*q => a_2 = 5*(-2) => a_2 = -10
a_3 = a_2*q => a_3 = -10*(-2) => a_3 = 20
a_4 = a_3*q => a_4 = 20*(-2) => a_4 =-40
a_5 = a_4*q => a_5 = -40*(-2) => a_5 = 80
Hence, evaluating the five terms of geometric sequence yields a_1 = 5, a_2 = -10, a_3 = 20, a_4 = -40, a_5 = 80.