If the image of the quadratic function y = x-(m+ 1) x-4 (m+5) intersects the X axis at two points, A is on the left side of the origin, B is on the right side of the origin, and OA: OB = 1: 4.

Oa: ob = 1: 4, set points A(-t, 0), B (4t, 0), t>0.

Then the relationship between the sum of the two roots is [m+ 1]=3t,

-t*4t=-4[m+5]

So m= 1 1, t= 4 or m=-4 t=- 1.

Therefore, m is 1 1 or -4.