In direct variation, we can express the relationship between \( y \) and \( x \) as follows:
\[ y = kx \]
where \( k \) is a constant.
Given that \( y = 5 \) when \( x = 55 \), we can substitute these values into the equation to find \( k \):
\[ 5 = k(55) \]
To solve for \( k \), we divide both sides by 55:
\[ k = \frac{5}{55} \]
Simplifying this gives:
\[ k = \frac{1}{11} \]
Now that we have \( k \), the equation relating \( y \) and \( x \) is:
\[ y = \frac{1}{11}x \]
Next, we need to find the value of \( y \) when \( x = 22 \). We substitute \( x = 22 \) into the equation:
\[ y = \frac{1}{11}(22) \]
Calculating this gives:
\[ y = \frac{22}{11} = 2 \]
Thus, the value of \( y \) when \( x = 22 \) is:
\[ \boxed{2} \]