Given the following recurrence relation: an=(−2)an−1, with a0=(−1) determine the value of a5

Technically you could answer this one by one, by substituting n with 1, 2, 3, 4, then 5. Like here:
A1=(-2)A1-1
=(-2)A0, then substituting A0 with -1...
=(-2)(-1)
Which would mean A1=2. Then..
A2=(-2)A2-1
A2=(-2)A1
A2=(-2)(2)
Which would mean A2=-4.
By repeating this process you'd eventually get A4..
A5=(-2)A4
if you did the steps right you'd get that A4 is -16..
A5=(-2)(-16).
Then simplify to get your answer.