The graph of 

y = |x - 4| - 5 

can be obtained from the graph of 

y = |x| as follows:

, which is the graph of y = |x| to this:

, which is the graph of y = |x| the above graph shrunk vertically by a factor or  to this:


, which is the graph of y = |x - 4|, the above graph shifted horizontally right 4 units to this:

, which is the graph of y = |x - 4|-5, the above graph shifted vertically down 5 units.

There is no reflecting in either axis.

Edwin