$\frac{5}{a^{2}+12 a+36}+\frac{8}{a^{2}-36}$

Step 1 ：Given the complex fraction \(\frac{5}{a^{2}+12 a+36}+\frac{8}{a^{2}-36}\)

Step 2 ：Factorize the denominators of the fractions. The denominator of the first fraction is a quadratic equation which can be factorized into \((a+6)^2\). The denominator of the second fraction is a difference of squares which can be factorized into \((a-6)(a+6)\).

Step 3 ：After factorizing, we can simplify the fraction by adding the numerators and denominators separately to get \(\frac{13a + 18}{(a - 6)(a + 6)^2}\)

Step 4 ：Final Answer: The simplified form of the given fraction is \(\boxed{\frac{13a + 18}{(a - 6)(a + 6)^2}}\)