SOLUTION
From the picture showing the graph,
the function
[tex]f(x)\text{ was firstly reflected horizontally. }[/tex]
This is represented as
[tex]-f(x)[/tex]
Then it was further translated by 5 units. That is vertical shift downwards. Giving us
[tex]-f(x)-5[/tex]
Hence the answer is
[tex]g(x)=-f(x)-5[/tex]
