It is a quadratic that opens down, therefore, find the maximum of the function by completing the square. Next check the endpoints of the domain for the lowest value, since it opens down, one of those x-values has the lowest part of the function for the range.

The maximum occurs at (2,1)... when x=0, y=-3, when x=5, y=-8, therefore the range is [-8,1] within that given domain.