Our starting function (the parent function) is  f(x) = x.


    Its first transformation is horizontal stretch by factor 5.

    For any function G(x), its horizontal stretch by factor k is the function G(x/k).
    Here factor k is a real number greater than 1.

        Do not miss it with the horizontal compressing by factor k: 
        horizontal compressing by factor k is another function, namely G(kx).

    So, after horizontal stretching, the parent function f(x) = x becomes function p(x) = f(x/5) = x/5.



    So, after first transformation our parent function  f(x) = x  is function p(x) = x/5.

    Again, our current function after first transformation is  p(x) = x/5.



    Second transformation is horizontal shift right 2 units.

    For any function G(x), its horizontal shift right 2 units is the function G(x-2).

        Do not miss it with horizontal shift left 2 units: 
        horizontal shift left 2 units is another function, namely G(x+2).

    So, after horizontal shift right 2 units, our current function p(x) = x/5 becomes function q(x) = (x-2)/5.


    It is our final function.


    AGAIN, our final function is q(x) = (x-2)/5.


ANSWER.  After two described transformations, the original parent function f(x) = x  becomes  q(x) = (x-2)/5.