I don't see any specific formula for f(x), so here's an example.
[tex]f(x)= x^{2} [/tex]
then translating down 5 units just subtracts 5 off the end of the formula. The translated function has formula
[tex]g(x)=x^2-5[/tex]
If your question is very general, and g(x) is the result of translating any old function f(x) down 5 units, then
g(x) = f(x) - 5
