Since the numbers are consecutive, they can be represented by:
x, x+1, x+2, x+3, x+4
Their sum is -20 = x+x+1+x+2+x+3+x+4. Result: -20=5x+10, or 5x=-30, or x = -6.
Then the numbers are -6, -5, -4, -3 and -2. These do add up to -20, as required.
The smallest of these is -6.