Step 1 :Find the value of \(g(5)\) by substituting \(x = 5\) into \(g(x) = x - 4\), which gives \(g(5) = 5 - 4 = 1\)
Step 2 :Find the value of \(f(5)\) by substituting \(x = 5\) into \(f(x) = (x + 6)(x + 3)\), which gives \(f(5) = (5 + 6)(5 + 3) = 11 * 8 = 88\)
Step 3 :Calculate \(\left(\frac{g}{f}\right)(5)\) by dividing \(g(5)\) by \(f(5)\), which gives \(\left(\frac{g}{f}\right)(5) = \frac{g(5)}{f(5)} = \frac{1}{88}\)
Step 4 :\(\boxed{\left(\frac{g}{f}\right)(5) = \frac{1}{88}}\)
Step 5 :Find the values of \(x\) that are not in the domain of \(\frac{g}{f}\) by setting \(f(x) = 0\) and solving for \(x\), which gives \((x + 6)(x + 3) = 0\)
Step 6 :Setting each factor equal to zero gives the solutions \(x = -6\) and \(x = -3\)
Step 7 :\(\boxed{\text{Values that are NOT in the domain of } \frac{g}{f}: -6, -3}\)