Given Information:
- A cube of side 5 has one vertex at the point (1,0,-1).
- Three edges from three vertices are parallel to the negative x and y axes and positive z axes.

To Find:
- The coordinates of the other vertices of the cube.

Approach:
1. Determine the position of the given vertex and the directions of the three edges.
2. Use the information to find the coordinates of the other vertices by adding or subtracting the side length from the given vertex.
3. Verify that the resulting points form a cube.

Solution:

1. Determine the position of the given vertex and the directions of the three edges:
The given vertex is (1,0,-1), and the three edges are:
- One edge parallel to the negative x-axis: This means that the x-coordinate remains constant while the y and z coordinates change. Let's call this vertex A.
- One edge parallel to the negative y-axis: This means that the y-coordinate remains constant while the x and z coordinates change. Let's call this vertex B.
- One edge parallel to the positive z-axis: This means that the z-coordinate remains constant while the x and y coordinates change. Let's call this vertex C.

2. Find the coordinates of the other vertices:
Since the side length of the cube is 5, we can find the coordinates of the other vertices using the following formulas:
- Vertex A: (1,0,-1)
- Vertex B: (1,0,-1) + (-5,0,0) = (-4,0,-1)
- Vertex C: (1,0,-1) + (0,-5,0) = (1,-5,-1)
- Vertex D: (1,0,-1) + (-5,0,0) + (0,-5,0) = (-4,-5,-1)
- Vertex E: (1,0,-1) + (0,0,5) = (1,0,4)
- Vertex F: (1,0,-1) + (-5,0,0) + (0,0,5) = (-4,0,4)
- Vertex G: (1,0,-1) + (0,-5,0) + (0,0,5) = (1,-5,4)
- Vertex H: (1,0,-1) + (-5,0,0) + (0,-5,0) + (0,0,5) = (-4,-5,4)

3. Verify that the resulting points form a cube:
To verify that the resulting points form a cube, we can check if the distance between any two vertices is equal to the side length (5 units). For example, we can calculate the distance between vertices A and B:

Distance AB = sqrt((x_B - x_A)^2 + (y_B - y_A)^2 + (z_B - z_A)^2)
= sqrt(((-4) - 1)^2 + (0 - 0)^2 + ((-1) - (-1))^2)
= sqrt((-5)^2 + 0 + 0)
= sqrt(25)
= 5

Since the distance between vertices A and

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