If \( z \) varies inversely as \( w^2 \), we can express this relationship as:
\[ z = \frac{k}{w^2} \]
where \( k \) is a constant.
From the information provided, we know that \( z = 20 \) when \( w = 2 \). We can use this to find the value of \( k \):
\[ 20 = \frac{k}{2^2} \]
This simplifies to:
\[ 20 = \frac{k}{4} \]
Multiplying both sides by 4 gives:
\[ k = 80 \]
Now that we have \( k \), we can use it to find \( z \) when \( w = 5 \):
\[ z = \frac{80}{5^2} \]
Calculating \( 5^2 \):
\[ 5^2 = 25 \]
So:
\[ z = \frac{80}{25} \]
This simplifies to:
\[ z = \frac{16}{5} = 3.2 \]
Thus, when \( w = 5 \), \( z = 3.2 \).