Step 1 :Define the functions \(f(x) = \frac{1}{x}\) and \(g(x) = \frac{x-4}{5}\).
Step 2 :Find the composition of the functions, which is \(f(g(x))\).
Step 3 :Simplify the composition of the functions to get \(f(g(x)) = \frac{5}{x - 4}\).
Step 4 :Find the domain of the function by setting the denominator equal to zero and solving for x, which gives \(x \neq 4\).
Step 5 :The simplified form of \(f(g(x))\) is \(\boxed{\frac{5}{x - 4}}\) and the domain is all real numbers except 4, so the final answer is \(\boxed{\frac{5}{x - 4}}\) and \(\boxed{x \neq 4}\).