Question

How does the graph of g(x)=x+5 compare to the graph of the parent function f(x)=x

Answer 1

The parent function $f(x)=x$ produces the straight line called line of odd quadrants that is symmetric relative to x & y axis.

The function $g(x)=x+5$ which can be rewritten as $g(x)=f(x)+5$ produces outputs always by 5 larger (shifts parent function up the y-axis by 5) than parent function however it's slope does not change the slope and the symmetry has vanished.

Hope this helps.