Let \( x \) be the total number of free throws Avani attempted.
Since Avani misses 5% of her free throws, the number of missed free throws can be expressed as:
\[ 0.05x \]
We know that Avani missed 4 free throws, so we can set up the equation:
\[ 0.05x = 4 \]
To find \( x \), divide both sides of the equation by 0.05:
\[ x = \frac{4}{0.05} \]
Calculating the right-hand side gives:
\[ x = 4 \div 0.05 = 4 \times \frac{100}{5} = 4 \times 20 = 80 \]
Thus, the total number of free throws Avani attempted is
\[ \boxed{80} \]