Yeah, I don't think it's quite right. A general point on the line is, fixing z=t. y=t-4 and x=3t+23. i.e. (3t+23,t-4,t). Or did I do that wrong? I would then take the difference between that and (4,5,5) and minimize the distance wrt to t. That would give you two points on the line, yes?
Well, from the given question it is evident that the equation which to be found is of a line. Now, the equation,
directly gives you the direction ratios of the required line, isnt it? What would they be?