To find the fraction of the total number of goats that ran away, we need to divide the number of goats that ran away by the total number of goats.
The total number of goats is 35, and the number of goats that ran away is 5.
So, the fraction is:
\[ \frac{5}{35} \]
Next, we can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 5:
\[ \frac{5 \div 5}{35 \div 5} = \frac{1}{7} \]
Therefore, the fraction of the total number of goats that ran away is \(\frac{1}{7}\).