Given that \(\lim_{x \to 5} f(x) = 3\) and \(\lim_{x \to 5} g(x) = 8\), evaluate \(\lim_{x \to 5} \frac{{f(x) + g(x)}}{{5f(x)}}\). If the limit does not exist, enter \DNE\. What is the value of the limit?
Options:
A) 11/15
B) 13/15
C) 17/15
D) DNE