-----------------------------------------------------
  -->  (1)   OR  (2) 
-----------------------------------------------------
(1):


  -->  (1a)   OR  (1b) 
(1a):    -->  
(1b):    -->  
-----------------------------------------------------
(2):


  -->  (1a)   OR  (1b) 
(1a):    -->  
(1b):    -->  
-----------------------------------------------------

    | 2*(|x-3|)-7 | < 5


is equivalent to


    -5 < 2*|x-3| - 7 < 5


is equivalent  (after adding 7 to each of 3 parts of the inequality)


    -5 + 7 < 2*|x-3| < 5 + 7


is the same as


    2 < 2*|x-3| < 12    


is equivalent to   (after dividing all the three terms of the inequality by 2)


    1 < |x-3| < 6.


The solutions to the last inequality are those values of x (those numbers or points in the number line) 
that are remoted from the point x= 3 farther than 1 unit and closer than 6 units.


Obviously, these points (numbers, solutions) are 


    -3 < x < 2   and/or  4 < x < 9.


ANSWER.  The solution set to the original inequality is the union  of two intervals  {-3,2)  and  (4,9):  (-3,2) U (4,9).