Line eq in 3D

I'll label your points A(5, 5, 5) and B(-8, -6, -3). Now, we need a direction vector, which will be AB (you can use BA if you want but I'll use AB):

AB = [-8-5 , -6-5 , -3-5]
AB = [-13, -11, -8]

Now that we have this, we'll use point A to find the equation of the line. I'm going to be finding the equation in parametric form (you can convert it to cartesian or vector later on if you wish):

The equation is given be:

x = x1 + at
y = y1 + bt
z = z1 + ct

Where the line goes through (x1, y1, z1) and has direction vector [a, b, c]

So, using your point (5, 5, 5) and direction vector [-13, -11, -8]:

x = 5 - 13t
y = 5 - 11t
z = 5 - 8t

Where t is the parameter and can take any real values.