The first 5 terms can be written:
a,a+d,a+2d,a+3d, a+4d where a is the first term and d is the difference.
So a+4d=8 (5th term) and
5a+10d=0 (sum of first 5 terms).
Therefore 5a=-10d, a=-2d.
So -2d+4d=8, 2d=8, d=4, making a=-8.
The series is:
-8, -4, 0, 4, 8,... First term: -8, difference=4.