Answer:
Stare at it long enough. You will notice that with each step you double the value, and change sign. It makes it a geometric sequence of ratio -2. At this point you have two ways of writing down:
Option 1: Ricorsively, the first term is -5, then the next term is -2 times the previous one:
Option 2: In closed form, remembering that the n-th term in a geometric sequence is the starting term times the n-th power of the ratio:
Either work, depending on what you need to use it for.