We can solve this for the common ratio , r
-4 (r)^5 = -12500 divide both sides by -4
r^5 = 3125 take the 5th root of both sides
r = 5
So the missing terms are
-20 -100 -500 -2500
I got r = 625 because I multiplied 1/5 times both sides. That was what I was taught but it didn't seem right. Shouldn't performing the square root and multiplying by 1/5 give me the same answer?