Step 1 :The function h(x) is a rational function, which means it's a ratio of two polynomials. To find h(5), we need to substitute x = 5 into the function and simplify the result.
Step 2 :Substitute x = 5 into the function: \[h(5)=\frac{5^{2}+5-12}{5^{2}-4 \times 5-12}\]
Step 3 :Simplify the result to get a decimal number: h(5) = -2.5714285714285716
Step 4 :Convert the decimal to a fraction to simplify the answer as much as possible: \[h(5) = -\frac{18}{7}\]
Step 5 :Final Answer: \[h(5) = \boxed{-\frac{18}{7}}\]