If we have the function y=f(x-5), why is it translated 5 units in the positive x direction? e. g. (2,0) becomes (7,0) but if we substitute x=2 into f(x-5) that becomes - 3 ?

See the attached diagram.in , the  manipulates what you put into the function.it will shift anything you put in 5 units to the left. this means that it lets you get features of a graph that are 5 units behind more earlier than usual, if you think of the positive x-direction as advancing in time.in the diagram, the blue arrows coming out of the graph of  represent where the input gets manipulated to in terms of the original untransformed graph of  . it gets manipulated 5 units behind what you inputted on for  .you can see that you have to get to x=5, otherwise it will get manipulated to an undefined point on the original function.so in summary, it puts things that are 5 units left from your input at a more earlier place than usual. this makes it a translation of 5 units left.