5. Because f(x) monotonically increases, when x tends to negative infinity, y tends to-1; When x tends to positive infinity, y tends to 1. So the range is (-1, 1).

6. The symmetry axis of g (x) =-2x2-8x+1is x=-2, so when x < At -2, G (x) monotonically increases; When x> is at -2, g(x) decreases monotonically. Therefore, when x < At -2, f(x) decreases monotonically; When x> is at -2, f(x) increases monotonically.